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diff --git a/_sources/notebooks/interface_to_spice.ipynb b/_sources/notebooks/interface_to_spice.ipynb
index 10f9c15..eb71feb 100644
--- a/_sources/notebooks/interface_to_spice.ipynb
+++ b/_sources/notebooks/interface_to_spice.ipynb
@@ -322,7 +322,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.3"
+   "version": "3.11.9"
   }
  },
  "nbformat": 4,
diff --git a/_sources/notebooks/udp_pl2pl.ipynb b/_sources/notebooks/udp_pl2pl.ipynb
index cb1af3c..380bbd6 100644
--- a/_sources/notebooks/udp_pl2pl.ipynb
+++ b/_sources/notebooks/udp_pl2pl.ipynb
@@ -8,7 +8,7 @@
     "\n",
     "In this tutorial we show the use of the {class}`pykep.trajopt.direct_pl2pl` to find a low-thrust trajectory connecting two moving planets. \n",
     "\n",
-    "The decision vector in this class compatible with {cite:p}`pagmo` UDPs (User Defined Problems) is:\n",
+    "The decision vector for this class, compatible with {cite:p}`pagmo` UDPs (User Defined Problems), is:\n",
     "\n",
     "$$\n",
     "\\mathbf x = [t_0, m_f, V_{sx}^\\infty, V^\\infty_{sy}, V^\\infty_{sz}, V^\\infty_{fx}, V^\\infty_{fy}, V^\\infty_{fz}, u_{x0}, u_{y0}, u_{z0}, u_{x1}, u_{y1}, u_{z1}, ..., T_{tof}]\n",
@@ -24,12 +24,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
-    "import pykep as _pk\n",
-    "import numpy as _np\n",
+    "import pykep as pk\n",
+    "import numpy as np\n",
     "import time\n",
     "import pygmo as pg\n",
     "import pygmo_plugins_nonfree as ppnf\n",
@@ -38,399 +38,299 @@
     "from matplotlib import pyplot as plt"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We start defining the problem data."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 68,
    "metadata": {},
-   "outputs": [
-    {
-     "ename": "AttributeError",
-     "evalue": "'pykep.core.planet' object has no attribute 'mu_central_body'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[1], line 7\u001b[0m\n\u001b[1;32m      4\u001b[0m earth \u001b[38;5;241m=\u001b[39m _pk\u001b[38;5;241m.\u001b[39mplanet(_pk\u001b[38;5;241m.\u001b[39mudpla\u001b[38;5;241m.\u001b[39mjpl_lp(body\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mEARTH\u001b[39m\u001b[38;5;124m\"\u001b[39m))\n\u001b[1;32m      5\u001b[0m mars \u001b[38;5;241m=\u001b[39m _pk\u001b[38;5;241m.\u001b[39mplanet(_pk\u001b[38;5;241m.\u001b[39mudpla\u001b[38;5;241m.\u001b[39mjpl_lp(body\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mMARS\u001b[39m\u001b[38;5;124m\"\u001b[39m))\n\u001b[0;32m----> 7\u001b[0m \u001b[38;5;28;43;01mclass\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;21;43;01mdirect_pl2pl\u001b[39;49;00m\u001b[43m:\u001b[49m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;250;43m    \u001b[39;49m\u001b[38;5;124;43;03m\"\"\"Represents the optimal low-thrust transfer between two :class:`~pykep.planet` using a direct method.\u001b[39;49;00m\n\u001b[1;32m      9\u001b[0m \n\u001b[1;32m     10\u001b[0m \u001b[38;5;124;43;03m    This problem works internally using the :class:`~pykep.leg.sims_flanagan` and manipulates its initial and final states, as well as its transfer time T, final mass mf\u001b[39;49;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     21\u001b[0m \n\u001b[1;32m     22\u001b[0m \u001b[38;5;124;43;03m    \"\"\"\u001b[39;49;00m\n\u001b[1;32m     24\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;28;43;01mdef\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;21;43m__init__\u001b[39;49m\u001b[43m(\u001b[49m\n\u001b[1;32m     25\u001b[0m \u001b[43m        \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m     26\u001b[0m \u001b[43m        \u001b[49m\u001b[43mpls\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mearth\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[43m        \u001b[49m\u001b[43mwith_gradient\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[1;32m     40\u001b[0m \u001b[43m    \u001b[49m\u001b[43m)\u001b[49m\u001b[43m:\u001b[49m\n",
-      "Cell \u001b[0;32mIn[1], line 29\u001b[0m, in \u001b[0;36mdirect_pl2pl\u001b[0;34m()\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mclass\u001b[39;00m \u001b[38;5;21;01mdirect_pl2pl\u001b[39;00m:\n\u001b[1;32m      8\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Represents the optimal low-thrust transfer between two :class:`~pykep.planet` using a direct method.\u001b[39;00m\n\u001b[1;32m      9\u001b[0m \n\u001b[1;32m     10\u001b[0m \u001b[38;5;124;03m    This problem works internally using the :class:`~pykep.leg.sims_flanagan` and manipulates its initial and final states, as well as its transfer time T, final mass mf\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     21\u001b[0m \n\u001b[1;32m     22\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[1;32m     24\u001b[0m     \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__init__\u001b[39m(\n\u001b[1;32m     25\u001b[0m         \u001b[38;5;28mself\u001b[39m,\n\u001b[1;32m     26\u001b[0m         pls\u001b[38;5;241m=\u001b[39mearth,\n\u001b[1;32m     27\u001b[0m         plf\u001b[38;5;241m=\u001b[39mmars,\n\u001b[1;32m     28\u001b[0m         ms\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1000\u001b[39m,\n\u001b[0;32m---> 29\u001b[0m         mu\u001b[38;5;241m=\u001b[39m\u001b[43mearth\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmu_central_body\u001b[49m(),\n\u001b[1;32m     30\u001b[0m         max_thrust\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.12\u001b[39m,\n\u001b[1;32m     31\u001b[0m         isp\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m3000\u001b[39m,\n\u001b[1;32m     32\u001b[0m         tof_bounds\u001b[38;5;241m=\u001b[39m[\u001b[38;5;241m80\u001b[39m, \u001b[38;5;241m400\u001b[39m],\n\u001b[1;32m     33\u001b[0m         mf_bounds\u001b[38;5;241m=\u001b[39m[\u001b[38;5;241m200.0\u001b[39m, \u001b[38;5;241m1000.0\u001b[39m],\n\u001b[1;32m     34\u001b[0m         nseg\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m10\u001b[39m,\n\u001b[1;32m     35\u001b[0m         cut\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.6\u001b[39m,\n\u001b[1;32m     36\u001b[0m         mass_scaling\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1000\u001b[39m,\n\u001b[1;32m     37\u001b[0m         r_scaling\u001b[38;5;241m=\u001b[39m_pk\u001b[38;5;241m.\u001b[39mAU,\n\u001b[1;32m     38\u001b[0m         v_scaling\u001b[38;5;241m=\u001b[39m_pk\u001b[38;5;241m.\u001b[39mEARTH_VELOCITY,\n\u001b[1;32m     39\u001b[0m         with_gradient\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m,\n\u001b[1;32m     40\u001b[0m     ):\n\u001b[1;32m     41\u001b[0m \u001b[38;5;250m        \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     42\u001b[0m \u001b[38;5;124;03m        Initializes the direct_point2point instance with given parameters.\u001b[39;00m\n\u001b[1;32m     43\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     72\u001b[0m \n\u001b[1;32m     73\u001b[0m \u001b[38;5;124;03m        \"\"\"\u001b[39;00m\n\u001b[1;32m     74\u001b[0m         \u001b[38;5;66;03m# We add as data member one single Sims-Flanagan leg using the problem data\u001b[39;00m\n\u001b[1;32m     75\u001b[0m         \u001b[38;5;66;03m# and some temporary (and unused, thus irrelelvant) values for the to-be-optimzed parameters throttles, tof and mf.\u001b[39;00m\n",
-      "\u001b[0;31mAttributeError\u001b[0m: 'pykep.core.planet' object has no attribute 'mu_central_body'"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "import numpy as _np\n",
-    "import pykep as _pk\n",
-    "\n",
-    "earth = _pk.planet(_pk.udpla.jpl_lp(body=\"EARTH\"))\n",
-    "mars = _pk.planet(_pk.udpla.jpl_lp(body=\"MARS\"))\n",
-    "\n",
-    "class direct_pl2pl:\n",
-    "    \"\"\"Represents the optimal low-thrust transfer between two :class:`~pykep.planet` using a direct method.\n",
-    "\n",
-    "    This problem works internally using the :class:`~pykep.leg.sims_flanagan` and manipulates its initial and final states, as well as its transfer time T, final mass mf\n",
-    "    and the controls as to link the two planets with a low-thrust trajectory.\n",
-    "\n",
-    "    It can be used to better profile and understand performances of optimizers on this type of direct approach, but has a limited use\n",
-    "    in the design of interplanetary trajectories as per the fixed point limitation.\n",
-    "\n",
-    "    The decision vector is::\n",
+    "# Problem data\n",
+    "mu = pk.MU_SUN\n",
+    "max_thrust = 0.3\n",
+    "isp = 3000\n",
     "\n",
-    "        z = [t0, mf, Vsx, Vsy, Vsz, Vfx, Vfy, Vfz, throttles, tof]\n",
+    "# Source and destination planets\n",
+    "earth = pk.planet_to_keplerian(\n",
+    "    pk.planet(pk.udpla.jpl_lp(body=\"EARTH\")), when=pk.epoch(5000)\n",
+    ")\n",
+    "mars = pk.planet_to_keplerian(\n",
+    "    pk.planet(pk.udpla.jpl_lp(body=\"MARS\")), when=pk.epoch(5000)\n",
+    ")\n",
     "\n",
-    "    where throttles is a vector of throttles structures as [u0x, u0y,u0z, ...]\n",
+    "# Initial state\n",
+    "ms = 1500.0\n",
     "\n",
-    "    \"\"\"\n",
+    "# Number of segments\n",
+    "nseg = 10"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We here instantiate two different versions of the same UDP (User Defined Problem), with analytical gradients and without. \n",
     "\n",
-    "    def __init__(\n",
-    "        self,\n",
+    "For the purpose of this simple notebook we choose a relatively simple Earth to Mars transfer with an initial $V_{\\infty}$ of 3 km/s."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "udp_nog = pk.trajopt.direct_pl2pl(\n",
     "        pls=earth,\n",
     "        plf=mars,\n",
-    "        ms=1000,\n",
-    "        max_thrust=0.12,\n",
+    "        ms=ms,\n",
+    "        mu=pk.MU_SUN,\n",
+    "        max_thrust=max_thrust,\n",
     "        isp=3000,\n",
-    "        t0_bounds=[4000, 5000],\n",
-    "        tof_bounds=[80, 400],\n",
-    "        mf_bounds=[200.0, 1000.0],\n",
-    "        vinf_dep=1e-3,\n",
-    "        vinf_arr=1e-3,\n",
-    "        nseg=10,\n",
+    "        t0_bounds=[6700.0, 6800.0],\n",
+    "        tof_bounds=[200.0, 300.0],\n",
+    "        mf_bounds=[1300., ms],\n",
+    "        vinfs=3.,\n",
+    "        vinff=0.,\n",
+    "        nseg=nseg,\n",
     "        cut=0.6,\n",
-    "        mass_scaling=1000,\n",
-    "        r_scaling=_pk.AU,\n",
-    "        v_scaling=_pk.EARTH_VELOCITY,\n",
+    "        mass_scaling=ms,\n",
+    "        r_scaling=pk.AU,\n",
+    "        v_scaling=pk.EARTH_VELOCITY,\n",
     "        with_gradient=False,\n",
-    "    ):\n",
-    "        \"\"\"\n",
-    "        Initializes the direct_pl2pl instance with given parameters.\n",
-    "\n",
-    "        Args:\n",
-    "            *rvs* (:class:`list`): Initial position and velocity vectors. Defaults to two vectors scaled by :class:`~pykep.AU` and Earth's velocity.\n",
-    "\n",
-    "            *rvf* (:class:`list`): Final position and velocity vectors. Defaults to two vectors scaled by :class:`~pykep.AU` and Earth's velocity.\n",
-    "\n",
-    "            *ms* (:class:`float`): Initial spacecraft mass in kg. Defaults to 1000 kg.\n",
-    "\n",
-    "            *mu* (:class:`float`): Gravitational parameter, default is for the Sun (:class:`~pykep.MU_SUN`).\n",
-    "\n",
-    "            *max_thrust* (:class:`float`): Maximum thrust in Newtons. Defaults to 0.12 N.\n",
-    "\n",
-    "            *isp* (:class:`float`): Specific impulse in seconds. Defaults to 3000 s.\n",
-    "            \n",
-    "            *t0_bounds* (:class:`list`): Bounds for departure epoch in MJD2000. Defaults to [4000, 5000] days.\n",
-    "\n",
-    "            *tof_bounds* (:class:`list`): Bounds for time of flight in days. Defaults to [0, 400] days.\n",
-    "\n",
-    "            *mf_bounds* (:class:`list`): Bounds for final mass in kg. Defaults to [200.0, 1000.0] kg.\n",
-    "            \n",
-    "            *vinf_dep* (:class:`float`): Allowed magnitude for the departure's relative velocity in km/s. Defaults to 1e-3.\n",
-    "\n",
-    "            *vinf_arr* (:class:`float`): Allowed magnitude for the arrival's relative velocity in km/s. Defaults to 1e-3.\n",
-    "\n",
-    "            *nseg* (:class:`int`): Number of segments for the trajectory. Defaults to 10.\n",
-    "\n",
-    "            *cut* (:class:`float`): Cut parameter for the :class:`~pykep.leg.sims_flanagan`. Defaults to 0.6.\n",
-    "\n",
-    "            *mass_scaling* (:class:`float`): Scaling factor for mass (used to scale constraints). Defaults to 1000.\n",
-    "\n",
-    "            *r_scaling* (:class:`float`): Scaling factor for distance, (used to scale constraints). Defaults AU (:class:`~pykep.AU`).\n",
-    "\n",
-    "            *v_scaling* (:class:`float`): Scaling factor for velocity (used to scale constraints). Defaults the Earth's velocity (:class:`~pykep.EARTH_VELOCITY`).\n",
-    "\n",
-    "            *with_gradient* (:class:`bool`): Indicates if gradient information should be used. Defaults True.\n",
-    "\n",
-    "        \"\"\"\n",
-    "        # We add as data member one single Sims-Flanagan leg using the problem data\n",
-    "        # and some temporary (and unused, thus irrelelvant) values for the to-be-optimzed parameters throttles, tof and mf.\n",
-    "        throttles = _np.random.uniform(-1, 1, size=(nseg * 3))\n",
-    "        self.leg = _pk.leg.sims_flanagan(\n",
-    "            rvs=rvs,\n",
-    "            ms=ms,\n",
-    "            throttles=throttles,\n",
-    "            rvf=rvf,\n",
-    "            mf=_np.mean(mf_bounds),\n",
-    "            tof=_np.mean(tof_bounds) * _pk.DAY2SEC,\n",
-    "            max_thrust=max_thrust,\n",
-    "            isp=isp,\n",
-    "            mu=mu,\n",
-    "            cut=cut,\n",
-    "        )\n",
-    "        self.tof_bounds = tof_bounds\n",
-    "        self.mf_bounds = mf_bounds\n",
-    "        self.mass_scaling = mass_scaling\n",
-    "        self.r_scaling = r_scaling\n",
-    "        self.v_scaling = v_scaling\n",
-    "        self.with_gradient = with_gradient\n",
-    "\n",
-    "    def get_bounds(self):\n",
-    "        lb = [self.mf_bounds[0]] + [-1, -1, -1] * self.leg.nseg + [self.tof_bounds[0]]\n",
-    "        ub = [self.mf_bounds[1]] + [1, 1, 1] * self.leg.nseg + [self.tof_bounds[1]]\n",
-    "        return (lb, ub)\n",
-    "\n",
-    "    def _set_leg_from_x(self, x):\n",
-    "        # We set the leg using data in the decision vector\n",
-    "        self.leg.tof = x[-1] * _pk.DAY2SEC\n",
-    "        self.leg.mf = x[0]\n",
-    "        self.leg.throttles = x[1:-1]\n",
-    "\n",
-    "    def fitness(self, x):\n",
-    "        # 1 - We set the leg using data in the decision vector\n",
-    "        self._set_leg_from_x(x)\n",
-    "        obj = -x[0] / self.mass_scaling\n",
-    "\n",
-    "        # 2 - We compute the constraints violations (mismatch+throttle)\n",
-    "        ceq = self.leg.compute_mismatch_constraints()\n",
-    "        cineq = self.leg.compute_throttle_constraints()\n",
-    "        retval = _np.array([obj] + ceq + cineq)  # here we can sum lists\n",
-    "\n",
-    "        # 3 - We scale the values in nd units (numerical solvers are sensitive to well-scaled values)\n",
-    "        retval[1:4] /= self.r_scaling\n",
-    "        retval[4:7] /= self.v_scaling\n",
-    "        retval[7] /= self.mass_scaling\n",
-    "\n",
-    "        return retval\n",
-    "\n",
-    "    def has_gradient(self):\n",
-    "        return self.with_gradient\n",
-    "\n",
-    "    def gradient(self, x):\n",
-    "        self._set_leg_from_x(x)\n",
-    "        _, mcg_xf, mcg_th_tof = self.leg.compute_mc_grad()\n",
-    "        tcg_th = self.leg.compute_tc_grad()\n",
-    "\n",
-    "        # 1 - The gradient of the objective function (obj = -mf)\n",
-    "        retval = [-1.0 / self.mass_scaling]\n",
-    "        # 2 - The gradient of the mismatch contraints (mcg). We divide them in pos, vel mass as they have different scaling units\n",
-    "        # pos\n",
-    "        for i in range(3):\n",
-    "            # First w.r.t. mf\n",
-    "            retval.append(mcg_xf[i, -1] / self.r_scaling)\n",
-    "            # Then the [throttles, tof]\n",
-    "            retval.extend(mcg_th_tof[i, :] / self.r_scaling)\n",
-    "            retval[-1] *= _pk.DAY2SEC\n",
-    "        # vel\n",
-    "        for i in range(3, 6):\n",
-    "            # First w.r.t. mf\n",
-    "            retval.append(mcg_xf[i, -1] / self.v_scaling)\n",
-    "            # Then the [throttles, tof]\n",
-    "            retval.extend(mcg_th_tof[i, :] / self.v_scaling)\n",
-    "            retval[-1] *= _pk.DAY2SEC\n",
-    "        # mass\n",
-    "        for i in range(6, 7):\n",
-    "            # First w.r.t. mf\n",
-    "            retval.append(mcg_xf[i, -1] / self.mass_scaling)\n",
-    "            # Then the [throttles, tof]\n",
-    "            retval.extend(mcg_th_tof[i, :] / self.mass_scaling)\n",
-    "            retval[-1] *= _pk.DAY2SEC\n",
-    "        # 3 -  The gradient of the throttle constraints\n",
-    "        for i in range(self.leg.nseg):\n",
-    "            retval.extend(tcg_th[i, 3 * i : 3 * i + 3])\n",
-    "\n",
-    "        return retval\n",
-    "\n",
-    "    def gradient_sparsity(self):\n",
-    "        dim = 2 + 3 * self.leg.nseg\n",
-    "        # The objective function only depends on the final mass, which is in the chromosome.\n",
-    "        retval = [[0, 0]]\n",
-    "        # The mismatch constraints depend on all variables.\n",
-    "        for i in range(1, 8):\n",
-    "            for j in range(dim):\n",
-    "                retval.append([i, j])\n",
-    "        # The throttle constraints only depend on the specific throttles (3).\n",
-    "        for i in range(self.leg.nseg):\n",
-    "            retval.append([8 + i, 3 * i + 1])\n",
-    "            retval.append([8 + i, 3 * i + 2])\n",
-    "            retval.append([8 + i, 3 * i + 3])\n",
-    "        # We return the sparsity pattern\n",
-    "        return retval\n",
-    "\n",
-    "    def get_nec(self):\n",
-    "        return 7\n",
-    "\n",
-    "    def get_nic(self):\n",
-    "        return self.leg.nseg\n",
-    "\n",
-    "    def pretty(self, x):\n",
-    "        \"\"\"\n",
-    "        Prints a detailed representation of the Point to point problem.\n",
-    "\n",
-    "        Args:\n",
-    "            *x* (:class:`list`): The decision vector containing final mass, thrust direction, and time of flight.\n",
-    "        \"\"\"\n",
-    "        self._set_leg_from_x(x)\n",
-    "        print(self.leg)\n",
-    "\n",
-    "    def plot(\n",
-    "        self,\n",
-    "        x,\n",
-    "        ax=None,\n",
-    "        units=_pk.AU,\n",
-    "        show_midpoints=False,\n",
-    "        show_gridpoints=False,\n",
-    "        show_throttles=False,\n",
-    "        length=0.1,\n",
-    "        arrow_length_ratio=0.05,\n",
-    "        **kwargs\n",
-    "    ):\n",
-    "        \"\"\"\n",
-    "        Plots the trajectory leg  3D axes.\n",
-    "\n",
-    "        Args:\n",
-    "            *x* (:class:`list`): The decision vector containing final mass, thrust direction, and time of flight.\n",
-    "\n",
-    "            *ax* (:class:`mpl_toolkits.mplot3d.axes3d.Axes3D`, optional): The 3D axis to plot on. Defaults to None.\n",
-    "\n",
-    "            *units* (:class:`float`, optional): The unit scale for the plot. Defaults to _pk.AU.\n",
-    "\n",
-    "            *show_midpoints* (:class:`bool`, optional): Whether to show midpoints on the trajectory. Defaults to False.\n",
-    "\n",
-    "            *show_gridpoints* (:class:`bool`, optional): Whether to show grid points on the trajectory. Defaults to False.\n",
-    "\n",
-    "            *show_throttles* (:class:`bool`, optional): Whether to show throttle vectors. Defaults to False.\n",
-    "\n",
-    "            *length* (:class:`float`, optional): Length of the throttle vectors. Defaults to 0.1.\n",
-    "\n",
-    "            *arrow_length_ratio* (:class:`float`, optional): Arrow length ratio for the throttle vectors. Defaults to 0.05.\n",
-    "\n",
-    "            *\\*\\*kwargs*: Additional keyword arguments for the plot.\n",
-    "\n",
-    "        Returns:\n",
-    "            :class:`mpl_toolkits.mplot3d.axes3d.Axes3D`: The 3D axis with the plotted trajectory.\n",
-    "        \"\"\"\n",
-    "        self._set_leg_from_x(x)\n",
-    "        sf = self.leg\n",
-    "        # Making the axis\n",
-    "        if ax is None:\n",
-    "            ax = _pk.plot.make_3Daxis(figsize=(7, 7))\n",
-    "\n",
-    "        rs, _ = sf.rvs\n",
-    "        rf, _ = sf.rvf\n",
-    "        ax.scatter(rs[0] / _pk.AU, rs[1] / units, rs[2] / units, c=\"k\", s=20)\n",
-    "        ax.scatter(rf[0] / _pk.AU, rf[1] / units, rf[2] / units, c=\"k\", s=20)\n",
+    ")\n",
     "\n",
-    "        # Plotting the trajctory leg\n",
-    "        ax = _pk.plot.add_sf_leg(\n",
-    "            ax,\n",
-    "            sf,\n",
-    "            units=units,\n",
-    "            show_throttles=show_throttles,\n",
-    "            length=length,\n",
-    "            show_gridpoints=show_gridpoints,\n",
-    "            show_midpoints=show_midpoints,\n",
-    "            arrow_length_ratio=arrow_length_ratio,\n",
-    "            **kwargs\n",
-    "        )\n",
+    "udp_g = pk.trajopt.direct_pl2pl(\n",
+    "        pls=earth,\n",
+    "        plf=mars,\n",
+    "        ms=ms,\n",
+    "        mu=pk.MU_SUN,\n",
+    "        max_thrust=max_thrust,\n",
+    "        isp=3000,\n",
+    "        t0_bounds=[6700.0, 6800.0],\n",
+    "        tof_bounds=[200.0, 300.0],\n",
+    "        mf_bounds=[1300., ms],\n",
+    "        vinfs=3.,\n",
+    "        vinff=0.,\n",
+    "        nseg=nseg,\n",
+    "        cut=0.6,\n",
+    "        mass_scaling=ms,\n",
+    "        r_scaling=pk.AU,\n",
+    "        v_scaling=pk.EARTH_VELOCITY,\n",
+    "        with_gradient=True,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Analytical performances of the analytical gradient\n",
     "\n",
-    "        return ax\n"
+    "And we take a quick look at the performances of the analytical gradient with respect to the numerically computed one."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 70,
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Problem data\n",
-    "mu = pk.MU_SUN\n",
-    "max_thrust = 0.12\n",
-    "isp = 3000\n",
-    "\n",
-    "# Initial state\n",
-    "ms = 1500.0\n",
-    "rs = np.array([1.2, 0.0, -0.01]) * pk.AU\n",
-    "vs = np.array([0.01, 1, -0.01]) * pk.EARTH_VELOCITY\n",
-    "\n",
-    "# Final state\n",
-    "mf = 1300.0\n",
-    "rf = np.array([1, 0.0, -0.0]) * pk.AU\n",
-    "vf = np.array([0.01, 1.1, -0.0]) * pk.EARTH_VELOCITY\n",
+    "# We need to generste a random chromosomes compatible with the UDP where to test the gradient.\n",
+    "prob_g = pg.problem(udp_g)\n",
+    "pop_g = pg.population(prob_g, 1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "First the analytical gradient:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 71,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "166 μs ± 239 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "udp_g.gradient(pop_g.champion_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Then a simple numerical gradient based on finite differences:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1.03 ms ± 618 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "pg.estimate_gradient(udp_g.fitness, pop_g.champion_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Then a higher order numerical gradient:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 73,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3.12 ms ± 34.8 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "pg.estimate_gradient_h(udp_g.fitness, pop_g.champion_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The analytical gradient its exact and faster, seems like a no brainer to use it. \n",
     "\n",
-    "# Throttles and tof\n",
-    "nseg = 4\n",
-    "throttles = np.random.uniform(-1, 1, size=(nseg * 3))\n",
-    "tof = 2 * np.pi * np.sqrt(pk.AU**3 / pk.MU_SUN) / 4\n",
+    "In reality, the effects on the optimization technique used are not straightforward, making the option to use numerical gradients still interesting in some, albeit rare, cases."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Solving the low-thrust transfer\n",
     "\n",
-    "udp_nog = pk.trajopt.direct_point2point(\n",
-    "    rvs=[rs, vs],\n",
-    "    rvf=[rf, vf],\n",
-    "    mu=pk.MU_SUN,\n",
-    "    max_thrust=0.22,\n",
-    "    isp=3000,\n",
-    "    tof_bounds=[200, 500],\n",
-    "    mf_bounds=[200.0, 1000.0],\n",
-    "    nseg=nseg,\n",
-    "    cut=0.6,\n",
-    "    with_gradient=False,\n",
-    ")\n",
+    "We define (again) the optimization problem, and set a tolerance for *pagmo* to be able to judge the relative value of two individuals. \n",
     "\n",
-    "udp_g = pk.trajopt.direct_point2point(\n",
-    "    rvs=[rs, vs],\n",
-    "    rvf=[rf, vf],\n",
-    "    mu=pk.MU_SUN,\n",
-    "    max_thrust=0.22,\n",
-    "    isp=3000,\n",
-    "    tof_bounds=[200, 500],\n",
-    "    mf_bounds=[200.0, 1000.0],\n",
-    "    nseg=nseg,\n",
-    "    cut=0.6,\n",
-    "    with_gradient=True,\n",
-    ")"
+    ":::{note}\n",
+    "This tolerance has a different role from the numerical tolerance set in the particular algorithm chosen to solve the problem and is only used by the *pagmo* machinery to decide outside the optimizer whether the new proposed indivdual is better than what was the previous *champion*."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 74,
    "metadata": {},
    "outputs": [],
    "source": [
-    "snopt72 = \"/usr/local/lib/libsnopt7_c.so\"\n",
+    "prob_g = pg.problem(udp_g)\n",
+    "prob_g.c_tol = 1e-6"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "... and we define an optimization algorithm."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 75,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "snopt72 = \"/Users/dario.izzo/opt/libsnopt7_c.dylib\"\n",
     "uda = ppnf.snopt7(library=snopt72, minor_version=2, screen_output=False)\n",
     "uda.set_integer_option(\"Major iterations limit\", 2000)\n",
     "uda.set_integer_option(\"Iterations limit\", 20000)\n",
     "uda.set_numeric_option(\"Major optimality tolerance\", 1e-3)\n",
-    "uda.set_numeric_option(\"Major feasibility tolerance\", 1e-12)\n",
+    "uda.set_numeric_option(\"Major feasibility tolerance\", 1e-11)\n",
     "\n",
-    "# uda = pg.nlopt(\"slsqp\")\n",
+    "#uda = pg.nlopt(\"slsqp\")\n",
     "algo = pg.algorithm(uda)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We solve the problem from random initial guess ten times and only save the result if a feasible solution is found (as defined by the criterias above)"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 76,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "True\n"
+      ".......x..\n",
+      "Best mass is:  1344.393538122888\n",
+      "Worst mass is:  1300.026710328152\n"
      ]
     }
    ],
    "source": [
-    "prob_nog = pg.problem(udp_nog)\n",
-    "prob_nog.c_tol = 1e-6\n",
-    "prob_g = pg.problem(udp_g)\n",
-    "prob_g.c_tol = 1e-6\n",
-    "pop_g = pg.population(prob_g, 1)\n",
-    "pop_g = algo.evolve(pop_g)\n",
-    "print(prob_g.feasibility_f(pop_g.champion_f))"
+    "masses = []\n",
+    "xs = []\n",
+    "for i in range(10):\n",
+    "    pop_g = pg.population(prob_g, 1)\n",
+    "    pop_g = algo.evolve(pop_g)\n",
+    "    if(prob_g.feasibility_f(pop_g.champion_f)):\n",
+    "        print(\".\", end=\"\")\n",
+    "        masses.append(pop_g.champion_x[1])\n",
+    "        xs.append(pop_g.champion_x)\n",
+    "    else:\n",
+    "        print(\"x\", end =\"\")\n",
+    "print(\"\\nBest mass is: \", np.max(masses))\n",
+    "print(\"Worst mass is: \", np.min(masses))\n",
+    "best_idx = np.argmax(masses)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And we plot the trajectory found:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 77,
    "metadata": {},
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Mismatch on pos: [ 1.57696078e-12  1.61709535e-12 -1.75156764e-13]\n",
-      "Mismatch on mass: 4.126786734559573e-08\n"
-     ]
-    },
     {
      "data": {
-      "image/png": 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",
       "text/plain": [
        "<Figure size 700x700 with 1 Axes>"
       ]
@@ -440,30 +340,40 @@
     }
    ],
    "source": [
-    "ax = udp_nog.plot(pop_g.get_x()[0], show_gridpoints=True)\n",
+    "ax = udp_g.plot(xs[best_idx], show_gridpoints=True)\n",
     "ax.view_init(90, 0)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Graident vs no gradient\n",
+    "We here take a look at the difference in solving the problem using the analytical gradient and not using it.\n",
+    "To do so we solve the same problem starting from 100 different initial guesses using both versions and compare."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 78,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "100%|██████████| 2000/2000 [02:18<00:00, 14.45it/s]"
+      "100%|██████████| 100/100 [02:09<00:00,  1.29s/it]"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Gradient: 1.8443e-02s\n",
-      "No Gradient: 3.0552e-02s\n",
-      "Gradient: 192\n",
-      "No Gradient: 188\n"
+      "Gradient: 4.8809e-01s\n",
+      "No Gradient: 5.5510e-01s\n",
+      "\n",
+      "Gradient (n.fails): 7\n",
+      "No Gradient (n.fails): 64\n"
      ]
     },
     {
@@ -483,25 +393,31 @@
     "fail_g = 0\n",
     "fail_nog = 0\n",
     "\n",
-    "for i in tqdm(range(2000)):\n",
-    "    pop_nog = pg.population(prob_nog, 1)\n",
+    "prob_g = pg.problem(udp_g)\n",
+    "prob_nog = pg.problem(udp_nog)\n",
+    "prob_g.c_tol = 1e-6\n",
+    "prob_nog.c_tol = 1e-6\n",
     "\n",
-    "    pop_g = pg.population(prob_g)\n",
-    "    pop_g.push_back(pop_nog.get_x()[0])\n",
+    "for i in tqdm(range(100)):\n",
+    "    pop_g = pg.population(prob_g, 1)\n",
+    "    pop_nog = pg.population(prob_nog)\n",
+    "    pop_nog.push_back(pop_g.champion_x)\n",
     "\n",
     "    start = time.time()\n",
     "    pop_g = algo.evolve(pop_g)\n",
     "    end = time.time()\n",
-    "    cpu_g.append(end - start)\n",
     "    if not prob_g.feasibility_f(pop_g.champion_f):\n",
     "        fail_g += 1\n",
+    "    else: # We only record the time for successfull attempts\n",
+    "        cpu_g.append(end - start)\n",
     "\n",
     "    start = time.time()\n",
     "    pop_nog = algo.evolve(pop_nog)\n",
     "    end = time.time()\n",
-    "    cpu_nog.append(end - start)\n",
     "    if not prob_nog.feasibility_f(pop_nog.champion_f):\n",
     "        fail_nog += 1\n",
+    "    else: # We only record the time for successfull attempts\n",
+    "        cpu_nog.append(end - start)\n",
     "\n",
     "print(f\"Gradient: {np.median(cpu_g):.4e}s\")\n",
     "print(f\"No Gradient: {np.median(cpu_nog):.4e}s\")\n",
@@ -512,12 +428,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 80,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "text/plain": [
+       "Text(0, 0.5, 'N. occurrences')"
+      ]
+     },
+     "execution_count": 80,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -529,8 +455,8 @@
    "source": [
     "cpu_g = np.array(cpu_g)\n",
     "cpu_nog = np.array(cpu_nog)\n",
-    "plt.hist(cpu_g[cpu_g < 0.2], bins=100, label=\"gradient\", density=True, alpha=0.5)\n",
-    "plt.hist(cpu_nog[cpu_nog < 0.2], bins=100, label=\"no_gradient\", density=True, alpha=0.5)\n",
+    "plt.hist(cpu_g[cpu_g < 2.2], bins=20, label=\"gradient\", density=True, alpha=0.5)\n",
+    "plt.hist(cpu_nog[cpu_nog < 1.2], bins=20, label=\"no_gradient\", density=True, alpha=0.5)\n",
     "# plt.xlim([0,0.15])\n",
     "plt.legend()\n",
     "plt.title(\"point2point, 4 seg case\")\n",
diff --git a/_sources/notebooks/udp_point2point.ipynb b/_sources/notebooks/udp_point2point.ipynb
index 0995ec0..8851b1c 100644
--- a/_sources/notebooks/udp_point2point.ipynb
+++ b/_sources/notebooks/udp_point2point.ipynb
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -91,11 +91,11 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
-    "snopt72 = \"/usr/local/lib/libsnopt7_c.so\"\n",
+    "snopt72 = \"/Users/dario.izzo/opt/libsnopt7_c.dylib\"\n",
     "uda = ppnf.snopt7(library=snopt72, minor_version=2, screen_output=False)\n",
     "uda.set_integer_option(\"Major iterations limit\", 2000)\n",
     "uda.set_integer_option(\"Iterations limit\", 20000)\n",
@@ -108,7 +108,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -131,12 +131,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
       "text/plain": [
        "<Figure size 700x700 with 1 Axes>"
       ]
@@ -152,25 +152,32 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "  0%|          | 0/2000 [00:00<?, ?it/s]\n"
+      "100%|██████████| 2000/2000 [04:06<00:00,  8.13it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Gradient: 5.6576e-02s\n",
+      "No Gradient: 5.9454e-02s\n",
+      "\n",
+      "Gradient (n.fails): 208\n",
+      "No Gradient (n.fails): 206\n"
      ]
     },
     {
-     "ename": "NameError",
-     "evalue": "name 'pg' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[2], line 10\u001b[0m\n\u001b[1;32m      7\u001b[0m fail_nog \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m tqdm(\u001b[38;5;28mrange\u001b[39m(\u001b[38;5;241m2000\u001b[39m)):\n\u001b[0;32m---> 10\u001b[0m     pop_nog \u001b[38;5;241m=\u001b[39m \u001b[43mpg\u001b[49m\u001b[38;5;241m.\u001b[39mpopulation(prob_nog, \u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m     12\u001b[0m     pop_g \u001b[38;5;241m=\u001b[39m pg\u001b[38;5;241m.\u001b[39mpopulation(prob_g)\n\u001b[1;32m     13\u001b[0m     pop_g\u001b[38;5;241m.\u001b[39mpush_back(pop_nog\u001b[38;5;241m.\u001b[39mget_x()[\u001b[38;5;241m0\u001b[39m])\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'pg' is not defined"
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
      ]
     }
    ],
@@ -212,12 +219,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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/v3MzZ840atWqZXh5eRmNGjUy3nvvPdv3NdtXX31ldOvWzahWrZrh6elp+Pv7G/fcc4/x/fff2+3v/PnzxksvvWQ0aNDA8PT0NPz8/IymTZsao0aNMpKTk28YL1CcLIbxjzFkAA6JiorS5MmT9eeff5pmrsHmzZvVsWNHrVy5Ur1793Z1OHl66623NHbsWB06dCjfk2/d1fTp0/XSSy/p6NGjBb5PDwBORQEowTZt2qThw4eXuKRm4cKFkv4+RXb16lV9++23euONN/TQQw+R1ACFRGIDoMRauXKlq0MoEB8fH82bN09HjhxRenq6atasqRdeeEEvvfSSq0MDSjxORQEAANPgcm8AAGAaJDYAAMA0SGwAAIBpmH7ycFZWlk6cOCGr1Wp3F04AAOC+DMPQuXPnFBQUdMMbV/6T6RObEydOqEaNGq4OAwAAFMCxY8ccug2C6RMbq9Uq6e83xtfX18XRAACA/EhLS1ONGjVsf8fzy/SJTfbpJ19fXxIbAABKGEenkTB5GAAAmAaJDQAAMA0SGwAAYBqmn2MDAHA/mZmZunr1qqvDgAt5eHiodOnSTm+XxAYAUGwMw1BycrLOnj3r6lDgBipUqKDAwECn3meOxAYAUGyykxp/f3/5+Phw49SblGEYunjxolJSUiRJVatWdVrbJDYAgGKRmZlpS2oqVark6nDgYt7e3pKklJQU+fv7O+20FJOHAQDFIntOjY+Pj4sjgbvI/i44c74ViQ0AoFhx+gnZiuK7QGIDAABMg8QGAAA3EhUVpebNm9uWBw8erPvuu89l8ZQ0TB4GALjcvNjfim1foyLrF9u+nOH111+XYRhObTMqKkpr1qzR7t27ndquOyCxAQDAya5cuSJPT0+ntOXn5+eUdm4WnIoCAOAGzp07pwEDBqhcuXKqWrWq5s2bp4iICI0cOVKSVKtWLU2dOlWDBw+Wn5+fHnvsMUnSCy+8oPr168vHx0e1a9fWxIkTc1wBNHPmTAUEBMhqteqRRx7R5cuX7dZfeyrKMAzNnj1btWvXlre3t5o1a6ZPP/3Utn7z5s2yWCzauHGjWrVqJR8fH7Vr104HDhyQJEVHR2vy5Mn65ZdfZLFYZLFYFB0d7fw3zUVIbAAAuIHRo0frxx9/1BdffKHY2Fh9//33+vnnn+3qvPrqq2rSpIl27typiRMnSpKsVquio6O1f/9+vf7663rvvfc0b9482zaffPKJJk2apGnTpmnHjh2qWrWq3nrrrTxjeemll7R48WItWrRI+/bt06hRo/TQQw9py5YtdvUmTJigOXPmaMeOHSpTpoyGDh0qSerbt6/GjBmjxo0b6+TJkzp58qT69u3rjLfJLXAqyk1ce365pJ0DBgCzOnfunGJiYrR06VJ16tRJkrR48WIFBQXZ1bvrrrv03HPP2ZW99NJLtp9r1aqlMWPGaMWKFRo7dqwkaf78+Ro6dKgeffRRSdLUqVP1zTff5Bi1yXbhwgXNnTtX3377rcLDwyVJtWvX1g8//KB33nlHHTp0sNWdNm2abXncuHHq3r27Ll++LG9vb5UvX15lypRRYGBgYd4at0Ri46Zym0hHsgMAxe/w4cO6evWqWrdubSvz8/NTgwYN7Oq1atUqx7affvqp5s+fr//97386f/68MjIy5Ovra1ufkJCgJ5980m6b8PBwbdq0KddY9u/fr8uXLysyMtKu/MqVK7r11lvtysLCwmw/Zz+yICUlRTVr1syruyUeiQ0AAHnIviLp2pvJXXulUrly5eyWt27dqn79+mny5Mnq2rWr/Pz8tHz5cs2ZM6fAsWRlZUmS/vOf/6hatWp267y8vOyWPTw8bD9nx569vZmR2AAAkIc6derIw8ND27dvV40aNSRJaWlpOnjwoN2pn2v9+OOPCg4O1oQJE2xlSUlJdnUaNWqkrVu3auDAgbayrVu3XrfN0NBQeXl56ejRo3nu+0Y8PT2VmZlZ4O3dGYkNAAB5sFqtGjRokJ5//nlVrFhR/v7+mjRpkkqVKpXnIwHq1q2ro0ePavny5brtttv0n//8R5999pldnREjRmjQoEFq1aqVbr/9di1ZskT79u1T7dq1rxvLc889p1GjRikrK0u333670tLSFBcXp/Lly2vQoEH56lOtWrWUmJio3bt3q3r16rJarTlGfEoqrooCAOAG5s6dq/DwcPXo0UOdO3dW+/bt1ahRI5UtW/a62/Ts2VOjRo3SM888o+bNmysuLs52tVS2vn376uWXX9YLL7ygli1bKikpSU899VSesbzyyit6+eWXNWPGDDVq1Ehdu3bVl19+qZCQkHz354EHHtDdd9+tjh07qkqVKlq2bFm+t3V3FsPZtzN0M2lpafLz81NqaqrdhC13k5+7bjJ5GEBJdvnyZSUmJiokJCTPhKAkuHDhgqpVq6Y5c+bokUcecXU4JVZe34mC/v3mVBQAADewa9cu/fe//1Xr1q2VmpqqKVOmSPp7VAbuhcQGAIB8eO2113TgwAF5enqqZcuW+v7771W5cmVXh4VrkNgAAHADt956q3bu3OnqMJAPTB4GAACmQWIDAABMw6WJTVRUlO3Jotmvfz63wjAMRUVFKSgoSN7e3oqIiNC+fftcGDEAAHBnLh+x+efTRU+ePKm9e/fa1s2ePVtz587VwoULFR8fr8DAQEVGRurcuXMujBgAALgrlyc22U8XzX5VqVJF0t+jNfPnz9eECRPUq1cvNWnSRDExMbp48aKWLl3q4qgBAIA7cnlic/DgQQUFBSkkJET9+vXT4cOHJUmJiYlKTk5Wly5dbHW9vLzUoUMHxcXFXbe99PR0paWl2b0AAMDNwaWJTZs2bfThhx9q/fr1eu+995ScnKx27drp1KlTSk5OliQFBATYbRMQEGBbl5sZM2bIz8/P9sp+YBkAAJA2b94si8Wis2fPSpKio6NVoUIFl8bkTC69j023bt1sPzdt2lTh4eGqU6eOYmJi1LZtW0m5PyY+r4eOjR8/XqNHj7Ytp6WlkdwAgLvbNKP49tVxfPHtqwTo27ev7rnnHqe2uXnzZnXs2FFnzpwp9qTJ5aei/qlcuXJq2rSpDh48aLs66trRmZSUlByjOP/k5eUlX19fuxcAAGZy5coVp7Xl7e0tf39/p7Xnam6V2KSnpyshIUFVq1ZVSEiIAgMDFRsba1t/5coVbdmyRe3atXNhlACAm01ERISGDx+usWPHqmLFigoMDFRUVJRt/dGjR9WzZ0+VL19evr6+6tOnj/744498tz916lT5+/vLarXq0Ucf1bhx49S8eXPb+sGDB+u+++7TjBkzFBQUpPr1/34o8scff6xWrVrJarUqMDBQ/fv3V0pKil3ba9euVf369eXt7a2OHTvqyJEjdutzOxX15ZdfqmXLlipbtqxq166tyZMnKyMjw7beYrHo3//+t+6//375+PioXr16+uKLLyRJR44cUceOHSVJt9xyiywWiwYPHpzv96KwXJrYPPfcc9qyZYsSExO1bds29e7dW2lpaRo0aJAsFotGjhyp6dOn67PPPtOvv/6qwYMHy8fHR/3793dl2ACAm1BMTIzKlSunbdu2afbs2ZoyZYpiY2NlGIbuu+8+nT59Wlu2bFFsbKwOHTqkvn375qvdJUuWaNq0aZo1a5Z27typmjVratGiRTnqbdy4UQkJCYqNjdVXX30l6e//8L/yyiv65ZdftGbNGiUmJtolEceOHVOvXr10zz33aPfu3bakKS/r16/XQw89pOHDh2v//v165513FB0drWnTptnVmzx5svr06aM9e/bonnvu0YABA3T69GnVqFFDq1atkiQdOHBAJ0+e1Ouvv56v98IZXDrH5vjx43rwwQf1119/qUqVKmrbtq22bt2q4OBgSdLYsWN16dIlDRs2TGfOnFGbNm20YcMGWa1WV4YNALgJhYWFadKkSZKkevXqaeHChdq4caMkac+ePUpMTLTN6fzoo4/UuHFjxcfH67bbbsuz3QULFuiRRx7RkCFDJEkvv/yyNmzYoPPnz9vVK1eunP7973/L09PTVjZ06FDbz7Vr19Ybb7yh1q1b6/z58ypfvrwWLVqk2rVra968ebJYLGrQoIH27t2rWbNmXTeeadOmady4cRo0aJCt3VdeeUVjx4619V/6exTpwQcflCRNnz5dCxYs0Pbt23X33XerYsWKkiR/f/9in2Pj0sRm+fLlea63WCyKioqyG+4DAMAVwsLC7JarVq2qlJQUJSQkqEaNGnYXqoSGhqpChQpKSEi4YWJz4MABDRs2zK6sdevW+vbbb+3KmjZtapfUSNKuXbsUFRWl3bt36/Tp08rKypL096mx0NBQJSQkqG3btnYX3YSHh+cZz86dOxUfH283QpOZmanLly/r4sWL8vHxyfF+lCtXTlarNcdpMFfg6d4AAOSDh4eH3bLFYlFWVtZ1r9a90VW817Z17bbXKleunN3yhQsX1KVLF3Xp0kUff/yxqlSpoqNHj6pr1662ycW5tXMjWVlZmjx5snr16pVjXdmyZW0/X+/9cDUSGwAACiE0NFRHjx7VsWPHbKM2+/fvV2pqqho1anTD7Rs0aKDt27fr4YcftpXt2LHjhtv997//1V9//aWZM2fa9nvtdqGhoVqzZo1d2datW/Nst0WLFjpw4IDq1q17wxiuJ3tkKTMzs8BtFJRbXRUFAEBJ07lzZ4WFhWnAgAH6+eeftX37dg0cOFAdOnRQq1atbrj9s88+q/fff18xMTE6ePCgpk6dqj179txwtKdmzZry9PTUggULdPjwYX3xxRd65ZVX7Oo8+eSTOnTokEaPHq0DBw5o6dKlio6OzrPdl19+WR9++KGioqK0b98+JSQkaMWKFXrppZdu2JdswcHBslgs+uqrr/Tnn3/mmC9UlEhsAAAoBIvFojVr1uiWW27RnXfeqc6dO6t27dpasWJFvrYfMGCAxo8fr+eee04tWrSwXdn0z9M+ualSpYqio6O1cuVKhYaGaubMmXrttdfs6tSsWVOrVq3Sl19+qWbNmuntt9/W9OnT82y3a9eu+uqrrxQbG6vbbrtNbdu21dy5c20X9uRHtWrVNHnyZI0bN04BAQF65pln8r1tYVmMgpyAK0HS0tLk5+en1NRUt75Z37zY325YZ1Rk/WKIBACKxuXLl5WYmKiQkJAb/tG+2UVGRiowMFAfffSRq0MpUnl9Jwr695s5NgAAuNDFixf19ttvq2vXripdurSWLVumb775xu4Gtcg/TkUBAFCEGjdurPLly+f6WrJkiSwWi9auXas77rhDLVu21JdffqlVq1apc+fOrg69RGLEBgCAIrR27VpdvXo113UBAQHy9vbWN998U8xRmReJDQAARciRSbcoPE5FAQCKlcmvWYEDiuK7QGIDACgW2XeqvXjxoosjgbvI/i5cexfjwuBUFACgWJQuXVoVKlSwPU/Ix8cn348cgLkYhqGLFy8qJSVFFSpUUOnSpZ3WNokNAKDYBAYGSpJbPCwRrlehQgXbd8JZSGwAAMXGYrGoatWq8vf3v+6VQrg5eHh4OHWkJhuJDQCg2JUuXbpI/qgBTB4GAACmQWIDAABMg1NRLpCfB14CAADHMWIDAABMg8QGAACYBokNAAAwDRIbAABgGiQ2AADANEhsAACAaZDYAAAA0yCxAQAApkFiAwAATIPEBgAAmAaJDQAAMA0SGwAAYBokNgAAwDRIbAAAgGmQ2AAAANMgsQEAAKZBYgMAAEyDxAYAAJgGiQ0AADANEhsAAGAaJDYAAMA0SGwAAIBpkNgAAADTILEBAACmQWIDAABMg8QGAACYBokNAAAwjTKuDgD5Ny/2N7vlUZH1XRQJAADuiREbAABgGiQ2AADANEhsAACAaZDYAAAA0yCxAQAApkFiAwAATIPEBgAAmAaJDQAAMA0SGwAAYBokNgAAwDTcJrGZMWOGLBaLRo4caSszDENRUVEKCgqSt7e3IiIitG/fPtcFCQAA3JpbJDbx8fF69913FRYWZlc+e/ZszZ07VwsXLlR8fLwCAwMVGRmpc+fOuShSAADgzlye2Jw/f14DBgzQe++9p1tuucVWbhiG5s+frwkTJqhXr15q0qSJYmJidPHiRS1dutSFEQMAAHfl8sTm6aefVvfu3dW5c2e78sTERCUnJ6tLly62Mi8vL3Xo0EFxcXHXbS89PV1paWl2LwAAcHMo48qdL1++XD///LPi4+NzrEtOTpYkBQQE2JUHBAQoKSnpum3OmDFDkydPdm6gAACgRHDZiM2xY8c0YsQIffzxxypbtux161ksFrtlwzBylP3T+PHjlZqaansdO3bMaTEDAAD35rIRm507dyolJUUtW7a0lWVmZuq7777TwoULdeDAAUl/j9xUrVrVViclJSXHKM4/eXl5ycvLq+gCBwAAbstlIzadOnXS3r17tXv3bturVatWGjBggHbv3q3atWsrMDBQsbGxtm2uXLmiLVu2qF27dq4KGwAAuDGXjdhYrVY1adLErqxcuXKqVKmSrXzkyJGaPn266tWrp3r16mn69Ony8fFR//79XREyAABwcy6dPHwjY8eO1aVLlzRs2DCdOXNGbdq00YYNG2S1Wl0dGgAAcEMWwzAMVwdRlNLS0uTn56fU1FT5+vq6OhxJ0rzY35zSzqjI+k5pBwAAd1PQv98uv48NAACAs5DYAAAA0yCxAQAApkFiAwAATIPEBgAAmAaJDQAAMA0SGwAAYBokNgAAwDRIbAAAgGmQ2AAAANMgsQEAAKbh1g/BRN5ye+YUz48CANzMGLEBAACmQWIDAABMg8QGAACYBokNAAAwDRIbAABgGiQ2AADANEhsAACAaZDYAAAA0yCxAQAApkFiAwAATIPEBgAAmAaJDQAAMA0SGwAAYBokNgAAwDRIbAAAgGk4nNhcunRJFy9etC0nJSVp/vz52rBhg1MDAwAAcJTDiU3Pnj314YcfSpLOnj2rNm3aaM6cOerZs6cWLVrk9AABAADyy+HE5ueff9Ydd9whSfr0008VEBCgpKQkffjhh3rjjTecHiAAAEB+OZzYXLx4UVarVZK0YcMG9erVS6VKlVLbtm2VlJTk9AABAADyy+HEpm7dulqzZo2OHTum9evXq0uXLpKklJQU+fr6Oj1AAACA/HI4sXn55Zf13HPPqVatWmrdurXCw8Ml/T16c+uttzo9QAAAgPwq4+gGvXv31u23366TJ0+qWbNmtvJOnTrp/vvvd2pwAAAAjijQfWwCAwNltVoVGxurS5cuSZJuu+02NWzY0KnBAQAAOMLhxObUqVPq1KmT6tevr3vuuUcnT56UJD366KMaM2aM0wMEAADIL4cTm1GjRsnDw0NHjx6Vj4+Prbxv375at26dU4OD4+bF/mb3AgDgZuLwHJsNGzZo/fr1ql69ul15vXr1uNwbAAC4lMMjNhcuXLAbqcn2119/ycvLyylBAQAAFITDic2dd95pe6SCJFksFmVlZenVV19Vx44dnRocAACAIxw+FfXqq68qIiJCO3bs0JUrVzR27Fjt27dPp0+f1o8//lgUMQIAAOSLwyM2oaGh2rNnj1q3bq3IyEhduHBBvXr10q5du1SnTp2iiBEAACBfHB6xkf6+j83kyZOdHQsAAEChODxis3jxYq1cuTJH+cqVKxUTE+OUoAAAAArC4cRm5syZqly5co5yf39/TZ8+3SlBAQAAFITDp6KSkpIUEhKSozw4OFhHjx51SlBmw43yAAAoHg6P2Pj7+2vPnj05yn/55RdVqlTJKUEBAAAUhMOJTb9+/TR8+HBt2rRJmZmZyszM1LfffqsRI0aoX79+RREjAABAvjh8Kmrq1KlKSkpSp06dVKbM35tnZWVp4MCBzLEBAAAu5XBi4+npqRUrVuiVV17RL7/8Im9vbzVt2lTBwcFFER8AAEC+Feg+NpJUv3591a9f35mxAAAAFIrDiU1mZqaio6O1ceNGpaSkKCsry279t99+67TgAAAAHOFwYjNixAhFR0ere/fuatKkiSwWS1HEBQAA4DCHE5vly5frk08+0T333FMU8QAAABSYw5d7e3p6qm7dukURCwAAQKE4nNiMGTNGr7/+ugzDKIp4AAAACszhxOaHH37QkiVLVKdOHd17773q1auX3csRixYtUlhYmHx9feXr66vw8HB9/fXXtvWGYSgqKkpBQUHy9vZWRESE9u3b52jIAADgJuHwHJsKFSro/vvvd8rOq1evrpkzZ9pObcXExKhnz57atWuXGjdurNmzZ2vu3LmKjo5W/fr1NXXqVEVGRurAgQOyWq1OicFM2h591255a83HXRQJAACu4XBis3jxYqft/N5777VbnjZtmhYtWqStW7cqNDRU8+fP14QJE2wjQTExMQoICNDSpUv1xBNPOC0OAABgDgW6QV9GRoY2b96sQ4cOqX///rJarTpx4oR8fX1Vvnz5AgWSmZmplStX6sKFCwoPD1diYqKSk5PVpUsXWx0vLy916NBBcXFx101s0tPTlZ6ebltOS0srUDxm0Pbou/rp/f9/OXsEZ1QkN1YEAJiTw4lNUlKS7r77bh09elTp6emKjIyU1WrV7NmzdfnyZb399tsOtbd3716Fh4fr8uXLKl++vD777DOFhoYqLi5OkhQQEGBXPyAgQElJSddtb8aMGZo8ebKj3QIAACbg8OThESNGqFWrVjpz5oy8vb1t5ffff782btzocAANGjTQ7t27tXXrVj311FMaNGiQ9u/fb1t/7Q0ADcPI86aA48ePV2pqqu117Ngxh2MCAAAlk8MjNj/88IN+/PFHeXp62pUHBwfr999/dziAf94Xp1WrVoqPj9frr7+uF154QZKUnJysqlWr2uqnpKTkGMX5Jy8vL3l5eTkcBwAAKPkcHrHJyspSZmZmjvLjx4875UolwzCUnp6ukJAQBQYGKjY21rbuypUr2rJli9q1a1fo/QAAAPNxOLGJjIzU/PnzbcsWi0Xnz5/XpEmTHH7Mwosvvqjvv/9eR44c0d69ezVhwgRt3rxZAwYMkMVi0ciRIzV9+nR99tln+vXXXzV48GD5+Piof//+joYNAABuAg6fipo7d67uuusuhYaG6vLly+rfv78OHjyoypUra9myZQ619ccff+jhhx/WyZMn5efnp7CwMK1bt06RkZGSpLFjx+rSpUsaNmyYzpw5ozZt2mjDhg3cwwYAAOTKYhTg2QiXLl3S8uXLtXPnTmVlZalFixYaMGCA3WRid5GWliY/Pz+lpqbK19fXJTHMi/2tWPZz7Q36rsXl3gCAkqKgf78dGrG5evWqGjRooK+++kpDhgzRkCFDHA4UAACgqDg0x8bDw0Pp6el5Xm4NAADgKg5PHn722Wc1a9YsZWRkFEU8AAAABebw5OFt27Zp48aN2rBhg5o2bapy5crZrV+9erXTggMAAHBEgZ7u/cADDxRFLAAAAIXiUGKTkZGhiIgIde3aVYGBgUUVEwAAQIE4NMemTJkyeuqpp+yeng0AAOAuHJ483KZNG+3atasoYgEAACgUh+fYDBs2TGPGjNHx48fVsmXLHJOHw8LCnBYcru9GN+Nzmk0z7Jc7ji+e/QIAUAAOJzZ9+/aVJA0fPtxWZrFYZBiGLBZLrg/IBAAAKA4OJzaJiYlFEQcAAEChOZzYBAcHF0UcAAAAheZwYvPhhx/muX7gwIEFDgZFyzYvZ1Olv/9lvgwAwGQcTmxGjBhht3z16lVdvHhRnp6e8vHxIbEBAAAu43Bic+bMmRxlBw8e1FNPPaXnn3/eKUGhBLv2KiqJkSEAQLFx+D42ualXr55mzpyZYzQHAACgODklsZGk0qVL68SJE85qDgAAwGEOn4r64osv7JYNw9DJkye1cOFCtW/f3mmBAQAAOMrhxOa+++6zW7ZYLKpSpYruuusuzZkzx1lxAQAAOMzhxCYrK6so4gAAACg0hxMbmFxuVzUBAFBCODx5uHfv3po5c2aO8ldffVX/+te/nBIUAABAQTic2GzZskXdu3fPUX733Xfru+++c0pQAAAABeHwqajz58/L09MzR7mHh4fS0tKcEhSK1k+HT0mStmb8JkkaFVnfleEAAOA0Do/YNGnSRCtWrMhRvnz5coWGhjolKAAAgIJweMRm4sSJeuCBB3To0CHdddddkqSNGzdq2bJlWrlypdMDRNHJ8VBMAABKOIcTm//3//6f1qxZo+nTp+vTTz+Vt7e3wsLC9M0336hDhw5FESMAAEC+FOhy7+7du+c6gRgAAMCVHJ5jEx8fr23btuUo37Ztm3bs2OGUoAAAAArC4cTm6aef1rFjx3KU//7773r66aedEhQAAEBBOJzY7N+/Xy1atMhRfuutt2r//v1OCQoAAKAgHE5svLy89Mcff+QoP3nypMqU4QkNAADAdRxObCIjIzV+/Hilpqbays6ePasXX3xRkZGRTg0OAADAEQ4PscyZM0d33nmngoODdeutt0qSdu/erYCAAH300UdODxAAACC/HE5sqlWrpj179mjJkiX65Zdf5O3trSFDhujBBx+Uh4dHUcQIAACQLwWaFFOuXDk9/vjjzo4FAACgUAqU2Bw6dEjz589XQkKCLBaLGjVqpBEjRqhOnTrOjg/uZtMM++WO410TBwAAuXB48vD69esVGhqq7du3KywsTE2aNNG2bdvUuHFjxcbGFkWMAAAA+eLwiM24ceM0atQozZw5M0f5Cy+8wJVRAADAZRwesUlISNAjjzySo3zo0KHcoA8AALiUw4lNlSpVtHv37hzlu3fvlr+/vzNiAgAAKBCHT0U99thjevzxx3X48GG1a9dOFotFP/zwg2bNmqUxY8YURYwAAAD54nBiM3HiRFmtVs2ZM0fjx/99RUxQUJCioqI0fPhwpwcIAACQXw4nNhaLRaNGjdKoUaN07tw5SZLVanV6YAAAAI4q1FMrSWiKT9uj77o6BAAA3J7Dk4cBAADcFYkNAAAwDRIbAABgGiQ2AADANJyW2OzYsUPfffeds5oDAABwWKGuivqnhx9+WL/99psyMzOd1SQAAIBDnJbYbNy4UVevXnVWcwAAAA5zWmITFBTkrKYAAAAKhMnDAADANPI9YlOqVClZLJY861gsFmVkZBQ6KAAAgILId2Lz2WefXXddXFycFixYIMMwnBIUAABAQeT7VFTPnj1zvBo0aKDo6GjNmTNH//rXv3TgwAGHdj5jxgzddtttslqt8vf313333ZejDcMwFBUVpaCgIHl7eysiIkL79u1zaD8AAODmUKA5NidOnNBjjz2msLAwZWRkaPfu3YqJiVHNmjUdamfLli16+umntXXrVsXGxiojI0NdunTRhQsXbHVmz56tuXPnauHChYqPj1dgYKAiIyNtTxYHAADI5tBVUampqZo+fboWLFig5s2ba+PGjbrjjjsKvPN169bZLS9evFj+/v7auXOn7rzzThmGofnz52vChAnq1auXJCkmJkYBAQFaunSpnnjiiQLvGwAAmE++R2xmz56t2rVr66uvvtKyZcsUFxdXqKQmN6mpqZKkihUrSpISExOVnJysLl262Op4eXmpQ4cOiouLc+q+AQBAyZfvEZtx48bJ29tbdevWVUxMjGJiYnKtt3r16gIFYhiGRo8erdtvv11NmjSRJCUnJ0uSAgIC7OoGBAQoKSkp13bS09OVnp5uW05LSytQPAAAoOTJd2IzcODAG17uXRjPPPOM9uzZox9++CHHumv3axjGdWOZMWOGJk+eXCQxAgAA95bvxCY6OrrIgnj22Wf1xRdf6LvvvlP16tVt5YGBgZL+HrmpWrWqrTwlJSXHKE628ePHa/To0bbltLQ01ahRo4gid562R9+1W95a83EXReKgTTNcHQEAADYuvfOwYRh65plntHr1an377bcKCQmxWx8SEqLAwEDFxsbayq5cuaItW7aoXbt2ubbp5eUlX19fuxcAALg5OO1ZUQXx9NNPa+nSpfr8889ltVptc2r8/Pzk7e0ti8WikSNHavr06apXr57q1aun6dOny8fHR/3793dl6AAAwA25NLFZtGiRJCkiIsKufPHixRo8eLAkaezYsbp06ZKGDRumM2fOqE2bNtqwYYOsVmsxRwsAANydSxOb/DyCwWKxKCoqSlFRUUUfEAAAKNF4ujcAADANEhsAAGAaJDYAAMA0SGwAAIBpkNgAAADTILEBAACmQWIDAABMg8QGAACYBokNAAAwDRIbAABgGi59pIIZzYv9zSnttD36rlPacUubZtgvdxzvmjgAAKbDiA0AADANRmxQ9K4doQEAoIgwYgMAAEyDxAYAAJgGiQ0AADANEhsAAGAaJDYAAMA0SGwAAIBpkNgAAADTILEBAACmQWIDAABMg8QGAACYBokNAAAwDRIbAABgGiQ2AADANHi6N/TT4VM5ysJrV3JBJAAAFA4jNgAAwDRIbAAAgGmQ2AAAANMgsQEAAKZBYgMAAEyDxAYAAJgGiQ0AADANEhsAAGAaJDYAAMA0uPMw3M+mGTnLOo4v/jgAACUOIzYAAMA0GLFBrq59flSRPjsqtxEaAAAKgBEbAABgGiQ2AADANEhsAACAaZDYAAAA0yCxAQAApkFiAwAATIPEBgAAmAaJDQAAMA0SGwAAYBokNgAAwDRIbAAAgGmQ2AAAANPgIZhwmmsfnCkV8cMzAQC4BokN8oWkBQBQEnAqCgAAmAaJDQAAMA0SGwAAYBouTWy+++473XvvvQoKCpLFYtGaNWvs1huGoaioKAUFBcnb21sRERHat2+fa4IFAABuz6WJzYULF9SsWTMtXLgw1/WzZ8/W3LlztXDhQsXHxyswMFCRkZE6d+5cMUcKAABKApdeFdWtWzd169Yt13WGYWj+/PmaMGGCevXqJUmKiYlRQECAli5dqieeeKI4QwUAACWA217unZiYqOTkZHXp0sVW5uXlpQ4dOiguLo7EBvY2zbBf7jjeNXEAAFzKbROb5ORkSVJAQIBdeUBAgJKSkq67XXp6utLT023LaWlpRRMgAABwO25/VZTFYrFbNgwjR9k/zZgxQ35+frZXjRo1ijpEAADgJtw2sQkMDJT0/4/cZEtJSckxivNP48ePV2pqqu117NixIo0TAAC4D7dNbEJCQhQYGKjY2Fhb2ZUrV7Rlyxa1a9fuutt5eXnJ19fX7gUAAG4OLp1jc/78ef3vf/+zLScmJmr37t2qWLGiatasqZEjR2r69OmqV6+e6tWrp+nTp8vHx0f9+/d3YdSF1/bou64OAQAAU3JpYrNjxw517NjRtjx69GhJ0qBBgxQdHa2xY8fq0qVLGjZsmM6cOaM2bdpow4YNslqtrgoZ/5DbgzEBAHAllyY2ERERMgzjuustFouioqIUFRVVfEEVAUZo3ISjl4RfWz8/2wAAXMpt59gAAAA4ym3vYwPY4QZ8AIB8YMQGAACYBiM2MKfc5scAAEyPERsAAGAajNigZGJEBgCQCxKbQpoX+5urQ3Br197rJrx2JRdFAgC4GXAqCgAAmAYjNihWud2tmFEcAICzkNgAzsT9dgDApTgVBQAATIPEBgAAmAaJDQAAMA0SGwAAYBpMHgYKgxsFAoBbYcQGAACYBokNAAAwDRIbAABgGsyxwc2Lm+kBgOkwYgMAAEyDxAYAAJgGiQ0AADAN5tjA5a594jdP+wYAFBSJDeDucrsJIBOdASBXJDYoERjVAQDkB4kNkI3HIwBAiUdiA7dz7egMAAD5xVVRAADANEhsAACAaZDYAAAA0yCxAQAApsHkYaC48fBNACgyjNgAAADTYMQGN5VC3+iPe90AgFtjxAYAAJgGIzaAu2FUCAAKjBEbAABgGozYAK7GCA0AOA2JTRFoe/RdV4dgevl5nhRPAAeAmw+nogAAgGkwYoObWm4jP9eO9OSnDgDAPZDYwLTyc7qqKPdF8gMAxY/EBrgZ5DZBmUc5ADAh5tgAAADTYMQGKErFdSl3QR6sycM4AZgQIzYAAMA0SGwAAIBpkNgAAADTYI4NUBK5y2MYmKcDwM0wYgMAAEyDERvgGvm5sZ+zbv53bTvc1A8ACofEBoB7udHpLW42CCAPJDZAEblZRmP+2c+tGb9JkkZF1ndVOABuciQ2AP5WkJGS4uCM/TIKBNw0SGwAN1LQh2nmGB3qWPj9Z4++ZGt79FS+4wEAVyGxAUqYfE1czmUEojhPjc2L/S3X8rZH3y2W/d9QfkaBiuNSdi6XNy8+W5cpEZd7v/XWWwoJCVHZsmXVsmVLff/9964OCQAAuCG3H7FZsWKFRo4cqbfeekvt27fXO++8o27dumn//v2qWbOmq8MDSqyCXrKe13b/HJEpKrmOPLlidCU/HIjjp8On7E7/XXcCtotGAnIbhbOLMT/vT8fxN27nZnaj9/D/Pmvew7y5/YjN3Llz9cgjj+jRRx9Vo0aNNH/+fNWoUUOLFi1ydWgAAMDNuPWIzZUrV7Rz506NGzfOrrxLly6Ki4tzUVRAwTjrpn7Fta/iGH25VkHiznWbw8/dcLtr5/jkZ+K2w5O7/+9/4Nnbba35uKTr/+/a7j3flM9J49f0NT9zl+ZlPJDn+rZH382lnby3uR679+zwc2qbW6VNub/P2e/XtbFJufezIPPIfjp8Ksd+imr043pzz7K1PXrK+XPPimCE79p+uNtokVsnNn/99ZcyMzMVEBBgVx4QEKDk5ORct0lPT1d6erptOTU1VZKUlpZWJDFevnA+R9mFS+m51AQKJu3CZbtls3y/ru2XVLx9y8/7WpA6ucneLvv3he330T+2vbZtR9p1dLvLGTl/b13b7rXt5LaN3e/V6+w3P5/p9d7nvH6/5uf7k9/38Nr9OOXvxbX7TkvLtT/XxpJnzP8XV27tXDfmXOIorCJ5v3KR3a5hGI5taLix33//3ZBkxMXF2ZVPnTrVaNCgQa7bTJo0yZDEixcvXrx48TLB69ixYw7lDm49YlO5cmWVLl06x+hMSkpKjlGcbOPHj9fo0aNty1lZWTp9+rQqVaoki8Vyw32mpaWpRo0aOnbsmHx9fQvXATd2s/RTunn6erP0U7p5+ko/zedm6asz+mkYhs6dO6egoCCHtnPrxMbT01MtW7ZUbGys7r//flt5bGysevbsmes2Xl5e8vLysiurUKGCw/v29fU19Zcu283ST+nm6evN0k/p5ukr/TSfm6Wvhe2nn5+fw9u4dWIjSaNHj9bDDz+sVq1aKTw8XO+++66OHj2qJ5980tWhAQAAN+P2iU3fvn116tQpTZkyRSdPnlSTJk20du1aBQcHuzo0AADgZtw+sZGkYcOGadiwYcWyLy8vL02aNCnH6SyzuVn6Kd08fb1Z+indPH2ln+Zzs/TVlf20GIaj11EBAAC4J7e/8zAAAEB+kdgAAADTILEBAACmQWIDAABMw3SJzVtvvaWQkBCVLVtWLVu21Pfff59n/S1btqhly5YqW7asateurbfffjtHnVWrVik0NFReXl4KDQ3VZ599Vuj9Fpaz+/nee+/pjjvu0C233KJbbrlFnTt31vbt2+3qREVFyWKx2L0CAwOd3rdrObuv0dHROfphsVh0+bL9M1VK+mcaERGRaz+7d+9uq1MSPtOTJ0+qf//+atCggUqVKqWRI0fmWq+kH6f56ae7HqfO7qe7HqOO7jM/fXXX49SRfq5evVqRkZGqUqWKfH19FR4ervXr1+eoV2zHaMGe4uSeli9fbnh4eBjvvfeesX//fmPEiBFGuXLljKSkpFzrHz582PDx8TFGjBhh7N+/33jvvfcMDw8P49NPP7XViYuLM0qXLm1Mnz7dSEhIMKZPn26UKVPG2Lp1a4H364797N+/v/Hmm28au3btMhISEowhQ4YYfn5+xvHjx211Jk2aZDRu3Ng4efKk7ZWSklIkfSzKvi5evNjw9fW168fJkycLtV937OepU6fs+vfrr78apUuXNhYvXmyrUxI+08TERGP48OFGTEyM0bx5c2PEiBE56pjhOM1PP93xOC2KfrrjMVqQfeanr+54nDrazxEjRhizZs0ytm/fbvz222/G+PHjDQ8PD+Pnn3+21SnOY9RUiU3r1q2NJ5980q6sYcOGxrhx43KtP3bsWKNhw4Z2ZU888YTRtm1b23KfPn2Mu+++265O165djX79+hV4v4VVFP28VkZGhmG1Wo2YmBhb2aRJk4xmzZoVPPACKIq+Ll682PDz83PqfgurOD7TefPmGVar1Th//rytrCR8pv/UoUOHXP84mOE4/afr9fNa7nCcFkU/3fEYLew+8/uZusNx6oz3NjQ01Jg8ebJtuTiPUdOcirpy5Yp27typLl262JV36dJFcXFxuW7z008/5ajftWtX7dixQ1evXs2zTnabBdlvYRRVP6918eJFXb16VRUrVrQrP3jwoIKCghQSEqJ+/frp8OHDhehN3oqyr+fPn1dwcLCqV6+uHj16aNeuXYXab2EU12f6/vvvq1+/fipXrpxdubt/pvlhhuO0IFx9nBZlP93pGC3Ofbr6OHVGP7OysnTu3Dm772VxHqOmSWz++usvZWZm5njqd0BAQI6ng2dLTk7OtX5GRob++uuvPOtkt1mQ/RZGUfXzWuPGjVO1atXUuXNnW1mbNm304Ycfav369XrvvfeUnJysdu3a6dSpU4XsVe6Kqq8NGzZUdHS0vvjiCy1btkxly5ZV+/btdfDgwQLvtzCK4zPdvn27fv31Vz366KN25SXhM80PMxynBeHq47So+ulux2hx7dMdjlNn9HPOnDm6cOGC+vTpYysrzmO0RDxSwREWi8Vu2TCMHGU3qn9teX7adHS/hVUU/cw2e/ZsLVu2TJs3b1bZsmVt5d26dbP93LRpU4WHh6tOnTqKiYnR6NGjC9SP/HB2X9u2bau2bdva1rdv314tWrTQggUL9MYbbxR4v4VVlJ/p+++/ryZNmqh169Z25SXlM3VWm+7+mTrCnY5TZ/fTXY/Rot6nOx2nBe3nsmXLFBUVpc8//1z+/v4Ot+mM99c0IzaVK1dW6dKlc2R2KSkpOTLAbIGBgbnWL1OmjCpVqpRnnew2C7LfwiiqfmZ77bXXNH36dG3YsEFhYWF5xlKuXDk1bdrU9r8oZyvqvmYrVaqUbrvtNls/zPaZXrx4UcuXL8/xv8DcuONnmh9mOE4d4S7HaXG9r64+Rotjn+5ynBamnytWrNAjjzyiTz75xG4UUSreY9Q0iY2np6datmyp2NhYu/LY2Fi1a9cu123Cw8Nz1N+wYYNatWolDw+PPOtkt1mQ/RZGUfVTkl599VW98sorWrdunVq1anXDWNLT05WQkKCqVasWoCc3VpR9/SfDMLR7925bP8z0mUrSJ598ovT0dD300EM3jMUdP9P8MMNxml/udJwW1/vq6mO0OPbpLsdpQfu5bNkyDR48WEuXLrW7VD1bsR6jDk01dnPZl4q9//77xv79+42RI0ca5cqVM44cOWIYhmGMGzfOePjhh231sy+ZHTVqlLF//37j/fffz3HJ7I8//miULl3amDlzppGQkGDMnDnzupeoXW+/JaGfs2bNMjw9PY1PP/3U7pLCc+fO2eqMGTPG2Lx5s3H48GFj69atRo8ePQyr1Vpk/SyqvkZFRRnr1q0zDh06ZOzatcsYMmSIUaZMGWPbtm353m9J6Ge222+/3ejbt2+u+y0Jn6lhGMauXbuMXbt2GS1btjT69+9v7Nq1y9i3b59tvRmO0/z00x2P06Lopzseo0XV12zudJw62s+lS5caZcqUMd5880277+XZs2dtdYrzGDVVYmMYhvHmm28awcHBhqenp9GiRQtjy5YttnWDBg0yOnToYFd/8+bNxq233mp4enoatWrVMhYtWpSjzZUrVxoNGjQwPDw8jIYNGxqrVq1yaL9Fwdn9DA4ONiTleE2aNMlWp2/fvkbVqlUNDw8PIygoyOjVq1euB6izObuvI0eONGrWrGl4enoaVapUMbp06WLExcU5tN+iUBTf3QMHDhiSjA0bNuS6z5Lymeb23QwODrarY4bj9Eb9dNfj1Nn9dNdj9Eb7LOh31x2PU0f62aFDh1z7OWjQILs2i+sYtRjG/804BAAAKOFMM8cGAACAxAYAAJgGiQ0AADANEhsAAGAaJDYAAMA0SGwAAIBpkNgAAADTILEBYFrR0dGqUKGCq8MAUIxIbAA4RXJysp599lnVrl1bXl5eqlGjhu69915t3LjRVqdWrVqyWCyyWCzy8fFRkyZN9M4779jWR0VFqXnz5jnaPnv2rCwWizZv3nzd/deqVUvz58+3K+vbt69+++23wnYNQAlSxtUBACj5jhw5ovbt26tChQqaPXu2wsLCdPXqVa1fv15PP/20/vvf/9rqTpkyRY899pjOnz+v6OhoPfnkk6pQoYL69u3r9Li8vb3l7e3t9HYBuC9GbAAU2rBhw2SxWLR9+3b17t1b9evXV+PGjTV69Ght3brVrq7ValVgYKDq1q2rqVOnql69elqzZk2h9h8REaGkpCSNGjXKNiIk5TwVlT0i9MEHH6hmzZoqX768nnrqKWVmZmr27NkKDAyUv7+/pk2bZtd+amqqHn/8cfn7+8vX11d33XWXfvnll0LFDKBoMGIDoFBOnz6tdevWadq0aSpXrlyO9Tea41K2bFldvXq1UDGsXr1azZo10+OPP67HHnssz7qHDh3S119/rXXr1unQoUPq3bu3EhMTVb9+fW3ZskVxcXEaOnSoOnXqpLZt28owDHXv3l0VK1bU2rVr5efnp3feeUedOnXSb7/9pooVKxYqdgDORWIDoFD+97//yTAMNWzY0KHtMjIy9PHHH2vv3r166qmnChVDxYoVVbp0adtoUF6ysrL0wQcfyGq1KjQ0VB07dtSBAwe0du1alSpVSg0aNNCsWbO0efNmtW3bVps2bdLevXuVkpIiLy8vSdJrr72mNWvW6NNPP9Xjjz9eqNgBOBeJDYBCMQxDkmynf27khRde0EsvvaT09HR5enrq+eef1xNPPFGUIdqpVauWrFarbTkgIEClS5dWqVKl7MpSUlIkSTt37tT58+dVqVIlu3YuXbqkQ4cOFU/QAPKNxAZAodSrV08Wi0UJCQm67777blj/+eef1+DBg+Xj46OqVavaJUS+vr5KTU3Nsc3Zs2clSX5+foWO18PDw27ZYrHkWpaVlSXp7xGeqlWr5npFFpeSA+6HxAZAoVSsWFFdu3bVm2++qeHDh+eYZ3P27Fm7BKBy5cqqW7durm01bNhQx48fV3Jyst0ppfj4eJUqVeq620mSp6enMjMzC9eZXLRo0ULJyckqU6aMatWq5fT2ATgXV0UBKLS33npLmZmZat26tVatWqWDBw8qISFBb7zxhsLDw/PdTpcuXdSoUSP169dPP/74oxITE/X555/rueee05NPPml3CulatWrV0nfffafff/9df/31lzO6JUnq3LmzwsPDdd9992n9+vU6cuSI4uLi9NJLL2nHjh1O2w8A5yCxAVBoISEh+vnnn9WxY0eNGTNGTZo0UWRkpDZu3KhFixblu50yZcpow4YNql27tgYMGKDGjRtr3LhxevTRRzV37tw8t50yZYqOHDmiOnXqqEqVKoXtko3FYtHatWt15513aujQoapfv7769eunI0eOKCAgwGn7AeAcFiN75h8AAEAJx4gNAAAwDRIbAABgGiQ2AADANEhsAACAaZDYAAAA0yCxAQAApkFiAwAATIPEBgAAmAaJDQAAMA0SGwAAYBokNgAAwDRIbAAAgGn8f/cG/LVEYtWgAAAAAElFTkSuQmCC",
+      "text/plain": [
+       "Text(0, 0.5, 'N. occurrences')"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -240,15 +257,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Number of segments: 4\n",
-       "Number of fwd segments: 2\n",
-       "Number of bck segments: 2\n",
+       "Number of segments: 2\n",
+       "Number of fwd segments: 1\n",
+       "Number of bck segments: 1\n",
        "Maximum thrust: 0.22\n",
        "Central body gravitational parameter: 1.32712440018e+20\n",
        "Specific impulse: 3000\n",
@@ -258,13 +275,13 @@
        "Final mass: 1\n",
        "State at departure: [[179517444840, 0, -1495978707], [297.8469183169681, 29784.691831696804, -297.8469183169681]]\n",
        "State at arrival: [[149597870700, 0, -0], [297.8469183169681, 32763.161014866488, -0]]\n",
-       "Throttles values: [-0.5531180194281187, 0.14971757884060444, 0.7940199350920427, 0.028288032565428445, -0.11046018798817858, -0.800424150704127, -0.6581747271243201, -0.5884590126432687, 0.9303693454363375, -0.7082653660632694, 0.3855806880092745, 0.3899050835184499]\n",
+       "Throttles values: [0, 0, 0, 0, 0, 0]\n",
        "\n",
-       "Mismatch constraints: [29919970440.50476, 38523538.099015325, -1496184052.1450462, -98.7230576541013, -2992.131264375472, -208.49434302739866, 998.99085894998]\n",
-       "Throttle constraints: [-0.04117744584645111, -0.34631951305277053, 0.6450650999139032, -0.19766173011602817]\n"
+       "Mismatch constraints: [29919941431.26764, 38529477.27626525, -1496162174.1910896, -6.189427009557562, -2978.469066381742, -297.82577960576987, 999]\n",
+       "Throttle constraints: [-1, -1]\n"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -273,13 +290,6 @@
     "udp_g.leg.tof=1232.\n",
     "udp_g.leg"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
diff --git a/_sources/trajopt.rst b/_sources/trajopt.rst
index 20913b5..3a267a8 100644
--- a/_sources/trajopt.rst
+++ b/_sources/trajopt.rst
@@ -18,5 +18,7 @@ Direct
 .. autoclass:: direct_point2point
     :members: pretty, plot
 
+.. autoclass:: direct_pl2pl
+    :members: pretty, plot
 
 
diff --git a/genindex.html b/genindex.html
index 46b6443..a82041e 100644
--- a/genindex.html
+++ b/genindex.html
@@ -421,6 +421,8 @@ <h2 id="D">D</h2>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="trajopt.html#pykep.trajopt.direct_pl2pl">direct_pl2pl (class in pykep.trajopt)</a>
+</li>
       <li><a href="trajopt.html#pykep.trajopt.direct_point2point">direct_point2point (class in pykep.trajopt)</a>
 </li>
   </ul></td>
@@ -677,12 +679,20 @@ <h2 id="P">P</h2>
 </li>
       <li><a href="planet.html#pykep.planet">planet (class in pykep)</a>
 </li>
+      <li><a href="trajopt.html#pykep.trajopt.direct_pl2pl.plot">plot() (pykep.trajopt.direct_pl2pl method)</a>
+
+      <ul>
+        <li><a href="trajopt.html#pykep.trajopt.direct_point2point.plot">(pykep.trajopt.direct_point2point method)</a>
+</li>
+      </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="trajopt.html#pykep.trajopt.direct_point2point.plot">plot() (pykep.trajopt.direct_point2point method)</a>
-</li>
-      <li><a href="trajopt.html#pykep.trajopt.direct_point2point.pretty">pretty() (pykep.trajopt.direct_point2point method)</a>
+      <li><a href="trajopt.html#pykep.trajopt.direct_pl2pl.pretty">pretty() (pykep.trajopt.direct_pl2pl method)</a>
+
+      <ul>
+        <li><a href="trajopt.html#pykep.trajopt.direct_point2point.pretty">(pykep.trajopt.direct_point2point method)</a>
 </li>
+      </ul></li>
       <li><a href="propagation.html#pykep.propagate_lagrangian">propagate_lagrangian() (in module pykep)</a>
 </li>
       <li><a href="propagation.html#pykep.propagate_lagrangian_v">propagate_lagrangian_v() (in module pykep)</a>
diff --git a/notebooks/anomalies.html b/notebooks/anomalies.html
index d7c939e..2dfdb6b 100644
--- a/notebooks/anomalies.html
+++ b/notebooks/anomalies.html
@@ -502,7 +502,7 @@ <h1>The various anomalies in pykep<a class="headerlink" href="#the-various-anoma
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>We solve 5941204 Kepler&#39;s Equations each second.
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>We solve 5935065 Kepler&#39;s Equations each second.
 </pre></div>
 </div>
 </div>
diff --git a/notebooks/epochs.html b/notebooks/epochs.html
index 0129940..005a5fa 100644
--- a/notebooks/epochs.html
+++ b/notebooks/epochs.html
@@ -526,7 +526,7 @@ <h2>Julian dates<a class="headerlink" href="#julian-dates" title="Permalink to t
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2024-06-28T11:09:56.527705
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2024-07-08T09:20:34.048868
 </pre></div>
 </div>
 </div>
diff --git a/notebooks/plotting.html b/notebooks/plotting.html
index 30871e8..84641ca 100644
--- a/notebooks/plotting.html
+++ b/notebooks/plotting.html
@@ -522,7 +522,26 @@ <h3>Plot planets<a class="headerlink" href="#plot-planets" title="Permalink to t
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/1f5b63d62e5a00cbc943106803267c6058880425dda5d7792e0483ba5c85cb49.png" src="../_images/1f5b63d62e5a00cbc943106803267c6058880425dda5d7792e0483ba5c85cb49.png" />
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">TypeError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="n">line</span> <span class="mi">3</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">make_3Daxis</span><span class="p">(</span><span class="n">figsize</span> <span class="o">=</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">ep</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">epoch</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<span class="ne">----&gt; </span><span class="mi">3</span> <span class="n">pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">add_solar_system</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">bodies</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">],</span> <span class="n">ep</span> <span class="o">=</span> <span class="n">ep</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="n">ax</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="mi">90</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">5</span> <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+<span class="nn">File ~/local/lib/python3.11/site-packages/pykep/plot/_planet.py:117,</span> in <span class="ni">add_solar_system</span><span class="nt">(ax, bodies, ep, s)</span>
+<span class="g g-Whitespace">    </span><span class="mi">115</span> <span class="k">if</span> <span class="mi">1</span> <span class="ow">in</span> <span class="n">bodies</span><span class="p">:</span>
+<span class="g g-Whitespace">    </span><span class="mi">116</span>     <span class="n">udpla</span> <span class="o">=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">udpla</span><span class="o">.</span><span class="n">jpl_lp</span><span class="p">(</span><span class="n">body</span><span class="o">=</span><span class="s2">&quot;Mercury&quot;</span><span class="p">)</span>
+<span class="ne">--&gt; </span><span class="mi">117</span>     <span class="n">mercury</span> <span class="o">=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">planet_to_keplerian</span><span class="p">(</span><span class="n">_pk</span><span class="o">.</span><span class="n">planet</span><span class="p">(</span><span class="n">udpla</span><span class="p">),</span> <span class="n">ep</span><span class="o">=</span><span class="n">ep</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">118</span>     <span class="n">_pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">add_planet_orbit</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">mercury</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">&quot;tomato&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;&quot;</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">119</span>     <span class="n">_pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">add_planet</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">mercury</span><span class="p">,</span> <span class="n">when</span><span class="o">=</span><span class="n">ep</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">&quot;tomato&quot;</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">&quot;Mercury&quot;</span><span class="p">)</span>
+
+<span class="ne">TypeError</span>: planet_to_keplerian() got an unexpected keyword argument &#39;ep&#39;
+</pre></div>
+</div>
+<img alt="../_images/96cac43e64f29eac6c718d74ff130cf052a7c9c6ecbf8ea79a015d4d489f4ba2.png" src="../_images/96cac43e64f29eac6c718d74ff130cf052a7c9c6ecbf8ea79a015d4d489f4ba2.png" />
 </div>
 </div>
 </section>
@@ -569,7 +588,7 @@ <h3>Plot a Lambert arc<a class="headerlink" href="#plot-a-lambert-arc" title="Pe
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/dce5c54680eea43a51eba7cca3eab836246e31e4cfc3ba68dbbb6deb0f916f60.png" src="../_images/dce5c54680eea43a51eba7cca3eab836246e31e4cfc3ba68dbbb6deb0f916f60.png" />
+<img alt="../_images/2cd6e41eb60a04d3a8c8e0f3dba65e341e47847492ac3fca079ff7590d2d620a.png" src="../_images/2cd6e41eb60a04d3a8c8e0f3dba65e341e47847492ac3fca079ff7590d2d620a.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -615,7 +634,7 @@ <h3>Plot a Lambert arc<a class="headerlink" href="#plot-a-lambert-arc" title="Pe
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/3546bb5597287ebfce28138d3f0c3301184f9b348b30652fd13a4ead1aeffd74.png" src="../_images/3546bb5597287ebfce28138d3f0c3301184f9b348b30652fd13a4ead1aeffd74.png" />
+<img alt="../_images/531d77567c1b90a85a7388a909c47d032a11aa15a46de162b0d14eda6e65bcba.png" src="../_images/531d77567c1b90a85a7388a909c47d032a11aa15a46de162b0d14eda6e65bcba.png" />
 </div>
 </div>
 </section>
@@ -659,7 +678,7 @@ <h3>Plot a Sims-Flanagan trajectory leg.<a class="headerlink" href="#plot-a-sims
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/b7988e5bd39d763183aca67a8f9c83ac6830064f7e1a5bd3c28d512a00444a3b.png" src="../_images/b7988e5bd39d763183aca67a8f9c83ac6830064f7e1a5bd3c28d512a00444a3b.png" />
+<img alt="../_images/a988b7d4757a7138202e15a39862388c23c170829066954c0ee7c871160e234f.png" src="../_images/a988b7d4757a7138202e15a39862388c23c170829066954c0ee7c871160e234f.png" />
 </div>
 </div>
 </section>
diff --git a/notebooks/propagate_lagrangian.html b/notebooks/propagate_lagrangian.html
index c2c7553..1dd4a62 100644
--- a/notebooks/propagate_lagrangian.html
+++ b/notebooks/propagate_lagrangian.html
@@ -478,7 +478,7 @@ <h1>Lagrange Propagation<a class="headerlink" href="#lagrange-propagation" title
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Only Keplerian Propagations
- Real time: 0.07442 seconds
+ Real time: 0.08034 seconds
 </pre></div>
 </div>
 </div>
@@ -497,7 +497,7 @@ <h1>Lagrange Propagation<a class="headerlink" href="#lagrange-propagation" title
 </div>
 <div class="cell_output docutils container">
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Keplerian Propagations with the STM computations
- Real time: 0.23353 seconds
+ Real time: 0.23731 seconds
 </pre></div>
 </div>
 </div>
diff --git a/notebooks/sims_flanagan_leg.html b/notebooks/sims_flanagan_leg.html
index 3ed9129..12f9f6f 100644
--- a/notebooks/sims_flanagan_leg.html
+++ b/notebooks/sims_flanagan_leg.html
@@ -502,7 +502,7 @@ <h1>The Sims-Flanagan trajectory leg<a class="headerlink" href="#the-sims-flanag
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/d70dbfca93a92ffeb2fa2af6b350d6cb30bb45aec2763c2c2d9de82f4f028807.png" src="../_images/d70dbfca93a92ffeb2fa2af6b350d6cb30bb45aec2763c2c2d9de82f4f028807.png" />
+<img alt="../_images/3749e58fcecefb63d415e0b714b69e9192e70263388392d014c8a7c1d59ce4a9.png" src="../_images/3749e58fcecefb63d415e0b714b69e9192e70263388392d014c8a7c1d59ce4a9.png" />
 </div>
 </div>
 </section>
diff --git a/notebooks/udp_pl2pl.html b/notebooks/udp_pl2pl.html
index fcb8f0a..c423263 100644
--- a/notebooks/udp_pl2pl.html
+++ b/notebooks/udp_pl2pl.html
@@ -396,7 +396,9 @@
   </button>
 `);
 </script>
-
+<button class="sidebar-toggle secondary-toggle btn btn-sm" title="Toggle secondary sidebar" data-bs-placement="bottom" data-bs-toggle="tooltip">
+    <span class="fa-solid fa-list"></span>
+</button>
 </div></div>
       
     </div>
@@ -412,6 +414,16 @@ <h1>Planet to planet low-thrust transfer</h1>
     <div id="print-main-content">
         <div id="jb-print-toc">
             
+            <div>
+                <h2> Contents </h2>
+            </div>
+            <nav aria-label="Page">
+                <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#analytical-performances-of-the-analytical-gradient">Analytical performances of the analytical gradient</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-the-low-thrust-transfer">Solving the low-thrust transfer</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#graident-vs-no-gradient">Graident vs no gradient</a></li>
+</ul>
+            </nav>
         </div>
     </div>
 </div>
@@ -423,8 +435,8 @@ <h1>Planet to planet low-thrust transfer</h1>
                   
   <section class="tex2jax_ignore mathjax_ignore" id="planet-to-planet-low-thrust-transfer">
 <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-planet-low-thrust-transfer" title="Permalink to this heading">#</a></h1>
-<p>In this tutorial we show the use of the <code class="xref py py-class docutils literal notranslate"><span class="pre">pykep.trajopt.direct_pl2pl</span></code> to find a low-thrust trajectory connecting two moving planets.</p>
-<p>The decision vector in this class compatible with <span id="id1">[<a class="reference internal" href="../bibliography.html#id9" title="Francesco Biscani and Dario Izzo. A parallel global multiobjective framework for optimization: pagmo. Journal of Open Source Software, 5(53):2338, 2020.">BI20</a>]</span> UDPs (User Defined Problems) is:</p>
+<p>In this tutorial we show the use of the <a class="reference internal" href="../trajopt.html#pykep.trajopt.direct_pl2pl" title="pykep.trajopt.direct_pl2pl"><code class="xref py py-class docutils literal notranslate"><span class="pre">pykep.trajopt.direct_pl2pl</span></code></a> to find a low-thrust trajectory connecting two moving planets.</p>
+<p>The decision vector for this class, compatible with <span id="id1">[<a class="reference internal" href="../bibliography.html#id9" title="Francesco Biscani and Dario Izzo. A parallel global multiobjective framework for optimization: pagmo. Journal of Open Source Software, 5(53):2338, 2020.">BI20</a>]</span> UDPs (User Defined Problems), is:</p>
 <div class="math notranslate nohighlight">
 \[
 \mathbf x = [t_0, m_f, V_{sx}^\infty, V^\infty_{sy}, V^\infty_{sz}, V^\infty_{fx}, V^\infty_{fy}, V^\infty_{fz}, u_{x0}, u_{y0}, u_{z0}, u_{x1}, u_{y1}, u_{z1}, ..., T_{tof}]
@@ -437,8 +449,8 @@ <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-p
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pykep</span> <span class="k">as</span> <span class="nn">_pk</span>
-<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">_np</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">pykep</span> <span class="k">as</span> <span class="nn">pk</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <span class="nn">time</span>
 <span class="kn">import</span> <span class="nn">pygmo</span> <span class="k">as</span> <span class="nn">pg</span>
 <span class="kn">import</span> <span class="nn">pygmo_plugins_nonfree</span> <span class="k">as</span> <span class="nn">ppnf</span>
@@ -449,387 +461,236 @@ <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-p
 </div>
 </div>
 </div>
+<p>We start defining the problem data.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">_np</span>
-<span class="kn">import</span> <span class="nn">pykep</span> <span class="k">as</span> <span class="nn">_pk</span>
-
-<span class="n">earth</span> <span class="o">=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">planet</span><span class="p">(</span><span class="n">_pk</span><span class="o">.</span><span class="n">udpla</span><span class="o">.</span><span class="n">jpl_lp</span><span class="p">(</span><span class="n">body</span><span class="o">=</span><span class="s2">&quot;EARTH&quot;</span><span class="p">))</span>
-<span class="n">mars</span> <span class="o">=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">planet</span><span class="p">(</span><span class="n">_pk</span><span class="o">.</span><span class="n">udpla</span><span class="o">.</span><span class="n">jpl_lp</span><span class="p">(</span><span class="n">body</span><span class="o">=</span><span class="s2">&quot;MARS&quot;</span><span class="p">))</span>
-
-<span class="k">class</span> <span class="nc">direct_pl2pl</span><span class="p">:</span>
-<span class="w">    </span><span class="sd">&quot;&quot;&quot;Represents the optimal low-thrust transfer between two :class:`~pykep.planet` using a direct method.</span>
-
-<span class="sd">    This problem works internally using the :class:`~pykep.leg.sims_flanagan` and manipulates its initial and final states, as well as its transfer time T, final mass mf</span>
-<span class="sd">    and the controls as to link the two planets with a low-thrust trajectory.</span>
-
-<span class="sd">    It can be used to better profile and understand performances of optimizers on this type of direct approach, but has a limited use</span>
-<span class="sd">    in the design of interplanetary trajectories as per the fixed point limitation.</span>
-
-<span class="sd">    The decision vector is::</span>
-
-<span class="sd">        z = [t0, mf, Vsx, Vsy, Vsz, Vfx, Vfy, Vfz, throttles, tof]</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Problem data</span>
+<span class="n">mu</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span>
+<span class="n">max_thrust</span> <span class="o">=</span> <span class="mf">0.3</span>
+<span class="n">isp</span> <span class="o">=</span> <span class="mi">3000</span>
 
-<span class="sd">    where throttles is a vector of throttles structures as [u0x, u0y,u0z, ...]</span>
+<span class="c1"># Source and destination planets</span>
+<span class="n">earth</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">planet_to_keplerian</span><span class="p">(</span>
+    <span class="n">pk</span><span class="o">.</span><span class="n">planet</span><span class="p">(</span><span class="n">pk</span><span class="o">.</span><span class="n">udpla</span><span class="o">.</span><span class="n">jpl_lp</span><span class="p">(</span><span class="n">body</span><span class="o">=</span><span class="s2">&quot;EARTH&quot;</span><span class="p">)),</span> <span class="n">when</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">epoch</span><span class="p">(</span><span class="mi">5000</span><span class="p">)</span>
+<span class="p">)</span>
+<span class="n">mars</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">planet_to_keplerian</span><span class="p">(</span>
+    <span class="n">pk</span><span class="o">.</span><span class="n">planet</span><span class="p">(</span><span class="n">pk</span><span class="o">.</span><span class="n">udpla</span><span class="o">.</span><span class="n">jpl_lp</span><span class="p">(</span><span class="n">body</span><span class="o">=</span><span class="s2">&quot;MARS&quot;</span><span class="p">)),</span> <span class="n">when</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">epoch</span><span class="p">(</span><span class="mi">5000</span><span class="p">)</span>
+<span class="p">)</span>
 
-<span class="sd">    &quot;&quot;&quot;</span>
+<span class="c1"># Initial state</span>
+<span class="n">ms</span> <span class="o">=</span> <span class="mf">1500.0</span>
 
-    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span>
-        <span class="bp">self</span><span class="p">,</span>
+<span class="c1"># Number of segments</span>
+<span class="n">nseg</span> <span class="o">=</span> <span class="mi">10</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>We here instantiate two different versions of the same UDP (User Defined Problem), with analytical gradients and without.</p>
+<p>For the purpose of this simple notebook we choose a relatively simple Earth to Mars transfer with an initial <span class="math notranslate nohighlight">\(V_{\infty}\)</span> of 3 km/s.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">udp_nog</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">trajopt</span><span class="o">.</span><span class="n">direct_pl2pl</span><span class="p">(</span>
         <span class="n">pls</span><span class="o">=</span><span class="n">earth</span><span class="p">,</span>
         <span class="n">plf</span><span class="o">=</span><span class="n">mars</span><span class="p">,</span>
-        <span class="n">ms</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
-        <span class="n">max_thrust</span><span class="o">=</span><span class="mf">0.12</span><span class="p">,</span>
+        <span class="n">ms</span><span class="o">=</span><span class="n">ms</span><span class="p">,</span>
+        <span class="n">mu</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span><span class="p">,</span>
+        <span class="n">max_thrust</span><span class="o">=</span><span class="n">max_thrust</span><span class="p">,</span>
         <span class="n">isp</span><span class="o">=</span><span class="mi">3000</span><span class="p">,</span>
-        <span class="n">t0_bounds</span><span class="o">=</span><span class="p">[</span><span class="mi">4000</span><span class="p">,</span> <span class="mi">5000</span><span class="p">],</span>
-        <span class="n">tof_bounds</span><span class="o">=</span><span class="p">[</span><span class="mi">80</span><span class="p">,</span> <span class="mi">400</span><span class="p">],</span>
-        <span class="n">mf_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">200.0</span><span class="p">,</span> <span class="mf">1000.0</span><span class="p">],</span>
-        <span class="n">vinf_dep</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
-        <span class="n">vinf_arr</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
-        <span class="n">nseg</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
+        <span class="n">t0_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">6700.0</span><span class="p">,</span> <span class="mf">6800.0</span><span class="p">],</span>
+        <span class="n">tof_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">200.0</span><span class="p">,</span> <span class="mf">300.0</span><span class="p">],</span>
+        <span class="n">mf_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">1300.</span><span class="p">,</span> <span class="n">ms</span><span class="p">],</span>
+        <span class="n">vinfs</span><span class="o">=</span><span class="mf">3.</span><span class="p">,</span>
+        <span class="n">vinff</span><span class="o">=</span><span class="mf">0.</span><span class="p">,</span>
+        <span class="n">nseg</span><span class="o">=</span><span class="n">nseg</span><span class="p">,</span>
         <span class="n">cut</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span>
-        <span class="n">mass_scaling</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span>
-        <span class="n">r_scaling</span><span class="o">=</span><span class="n">_pk</span><span class="o">.</span><span class="n">AU</span><span class="p">,</span>
-        <span class="n">v_scaling</span><span class="o">=</span><span class="n">_pk</span><span class="o">.</span><span class="n">EARTH_VELOCITY</span><span class="p">,</span>
+        <span class="n">mass_scaling</span><span class="o">=</span><span class="n">ms</span><span class="p">,</span>
+        <span class="n">r_scaling</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">AU</span><span class="p">,</span>
+        <span class="n">v_scaling</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">EARTH_VELOCITY</span><span class="p">,</span>
         <span class="n">with_gradient</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
-    <span class="p">):</span>
-<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="sd">        Initializes the direct_pl2pl instance with given parameters.</span>
-
-<span class="sd">        Args:</span>
-<span class="sd">            *rvs* (:class:`list`): Initial position and velocity vectors. Defaults to two vectors scaled by :class:`~pykep.AU` and Earth&#39;s velocity.</span>
-
-<span class="sd">            *rvf* (:class:`list`): Final position and velocity vectors. Defaults to two vectors scaled by :class:`~pykep.AU` and Earth&#39;s velocity.</span>
-
-<span class="sd">            *ms* (:class:`float`): Initial spacecraft mass in kg. Defaults to 1000 kg.</span>
-
-<span class="sd">            *mu* (:class:`float`): Gravitational parameter, default is for the Sun (:class:`~pykep.MU_SUN`).</span>
-
-<span class="sd">            *max_thrust* (:class:`float`): Maximum thrust in Newtons. Defaults to 0.12 N.</span>
-
-<span class="sd">            *isp* (:class:`float`): Specific impulse in seconds. Defaults to 3000 s.</span>
-<span class="sd">            </span>
-<span class="sd">            *t0_bounds* (:class:`list`): Bounds for departure epoch in MJD2000. Defaults to [4000, 5000] days.</span>
-
-<span class="sd">            *tof_bounds* (:class:`list`): Bounds for time of flight in days. Defaults to [0, 400] days.</span>
-
-<span class="sd">            *mf_bounds* (:class:`list`): Bounds for final mass in kg. Defaults to [200.0, 1000.0] kg.</span>
-<span class="sd">            </span>
-<span class="sd">            *vinf_dep* (:class:`float`): Allowed magnitude for the departure&#39;s relative velocity in km/s. Defaults to 1e-3.</span>
-
-<span class="sd">            *vinf_arr* (:class:`float`): Allowed magnitude for the arrival&#39;s relative velocity in km/s. Defaults to 1e-3.</span>
-
-<span class="sd">            *nseg* (:class:`int`): Number of segments for the trajectory. Defaults to 10.</span>
-
-<span class="sd">            *cut* (:class:`float`): Cut parameter for the :class:`~pykep.leg.sims_flanagan`. Defaults to 0.6.</span>
-
-<span class="sd">            *mass_scaling* (:class:`float`): Scaling factor for mass (used to scale constraints). Defaults to 1000.</span>
-
-<span class="sd">            *r_scaling* (:class:`float`): Scaling factor for distance, (used to scale constraints). Defaults AU (:class:`~pykep.AU`).</span>
-
-<span class="sd">            *v_scaling* (:class:`float`): Scaling factor for velocity (used to scale constraints). Defaults the Earth&#39;s velocity (:class:`~pykep.EARTH_VELOCITY`).</span>
-
-<span class="sd">            *with_gradient* (:class:`bool`): Indicates if gradient information should be used. Defaults True.</span>
-
-<span class="sd">        &quot;&quot;&quot;</span>
-        <span class="c1"># We add as data member one single Sims-Flanagan leg using the problem data</span>
-        <span class="c1"># and some temporary (and unused, thus irrelelvant) values for the to-be-optimzed parameters throttles, tof and mf.</span>
-        <span class="n">throttles</span> <span class="o">=</span> <span class="n">_np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">nseg</span> <span class="o">*</span> <span class="mi">3</span><span class="p">))</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">leg</span> <span class="o">=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">sims_flanagan</span><span class="p">(</span>
-            <span class="n">rvs</span><span class="o">=</span><span class="n">rvs</span><span class="p">,</span>
-            <span class="n">ms</span><span class="o">=</span><span class="n">ms</span><span class="p">,</span>
-            <span class="n">throttles</span><span class="o">=</span><span class="n">throttles</span><span class="p">,</span>
-            <span class="n">rvf</span><span class="o">=</span><span class="n">rvf</span><span class="p">,</span>
-            <span class="n">mf</span><span class="o">=</span><span class="n">_np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">mf_bounds</span><span class="p">),</span>
-            <span class="n">tof</span><span class="o">=</span><span class="n">_np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">tof_bounds</span><span class="p">)</span> <span class="o">*</span> <span class="n">_pk</span><span class="o">.</span><span class="n">DAY2SEC</span><span class="p">,</span>
-            <span class="n">max_thrust</span><span class="o">=</span><span class="n">max_thrust</span><span class="p">,</span>
-            <span class="n">isp</span><span class="o">=</span><span class="n">isp</span><span class="p">,</span>
-            <span class="n">mu</span><span class="o">=</span><span class="n">mu</span><span class="p">,</span>
-            <span class="n">cut</span><span class="o">=</span><span class="n">cut</span><span class="p">,</span>
-        <span class="p">)</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">tof_bounds</span> <span class="o">=</span> <span class="n">tof_bounds</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">mf_bounds</span> <span class="o">=</span> <span class="n">mf_bounds</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">mass_scaling</span> <span class="o">=</span> <span class="n">mass_scaling</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">r_scaling</span> <span class="o">=</span> <span class="n">r_scaling</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">v_scaling</span> <span class="o">=</span> <span class="n">v_scaling</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">with_gradient</span> <span class="o">=</span> <span class="n">with_gradient</span>
-
-    <span class="k">def</span> <span class="nf">get_bounds</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="n">lb</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mf_bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span> <span class="o">+</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">nseg</span> <span class="o">+</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">tof_bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
-        <span class="n">ub</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mf_bounds</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">nseg</span> <span class="o">+</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">tof_bounds</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
-        <span class="k">return</span> <span class="p">(</span><span class="n">lb</span><span class="p">,</span> <span class="n">ub</span><span class="p">)</span>
-
-    <span class="k">def</span> <span class="nf">_set_leg_from_x</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-        <span class="c1"># We set the leg using data in the decision vector</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">tof</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">_pk</span><span class="o">.</span><span class="n">DAY2SEC</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">mf</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">throttles</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-
-    <span class="k">def</span> <span class="nf">fitness</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-        <span class="c1"># 1 - We set the leg using data in the decision vector</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">_set_leg_from_x</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-        <span class="n">obj</span> <span class="o">=</span> <span class="o">-</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">mass_scaling</span>
-
-        <span class="c1"># 2 - We compute the constraints violations (mismatch+throttle)</span>
-        <span class="n">ceq</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">compute_mismatch_constraints</span><span class="p">()</span>
-        <span class="n">cineq</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">compute_throttle_constraints</span><span class="p">()</span>
-        <span class="n">retval</span> <span class="o">=</span> <span class="n">_np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">obj</span><span class="p">]</span> <span class="o">+</span> <span class="n">ceq</span> <span class="o">+</span> <span class="n">cineq</span><span class="p">)</span>  <span class="c1"># here we can sum lists</span>
-
-        <span class="c1"># 3 - We scale the values in nd units (numerical solvers are sensitive to well-scaled values)</span>
-        <span class="n">retval</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">4</span><span class="p">]</span> <span class="o">/=</span> <span class="bp">self</span><span class="o">.</span><span class="n">r_scaling</span>
-        <span class="n">retval</span><span class="p">[</span><span class="mi">4</span><span class="p">:</span><span class="mi">7</span><span class="p">]</span> <span class="o">/=</span> <span class="bp">self</span><span class="o">.</span><span class="n">v_scaling</span>
-        <span class="n">retval</span><span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="o">/=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mass_scaling</span>
-
-        <span class="k">return</span> <span class="n">retval</span>
-
-    <span class="k">def</span> <span class="nf">has_gradient</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">with_gradient</span>
-
-    <span class="k">def</span> <span class="nf">gradient</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">_set_leg_from_x</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-        <span class="n">_</span><span class="p">,</span> <span class="n">mcg_xf</span><span class="p">,</span> <span class="n">mcg_th_tof</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">compute_mc_grad</span><span class="p">()</span>
-        <span class="n">tcg_th</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">compute_tc_grad</span><span class="p">()</span>
-
-        <span class="c1"># 1 - The gradient of the objective function (obj = -mf)</span>
-        <span class="n">retval</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">1.0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">mass_scaling</span><span class="p">]</span>
-        <span class="c1"># 2 - The gradient of the mismatch contraints (mcg). We divide them in pos, vel mass as they have different scaling units</span>
-        <span class="c1"># pos</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">):</span>
-            <span class="c1"># First w.r.t. mf</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">mcg_xf</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">r_scaling</span><span class="p">)</span>
-            <span class="c1"># Then the [throttles, tof]</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">mcg_th_tof</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">r_scaling</span><span class="p">)</span>
-            <span class="n">retval</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">DAY2SEC</span>
-        <span class="c1"># vel</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">):</span>
-            <span class="c1"># First w.r.t. mf</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">mcg_xf</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">v_scaling</span><span class="p">)</span>
-            <span class="c1"># Then the [throttles, tof]</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">mcg_th_tof</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">v_scaling</span><span class="p">)</span>
-            <span class="n">retval</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">DAY2SEC</span>
-        <span class="c1"># mass</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">):</span>
-            <span class="c1"># First w.r.t. mf</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">mcg_xf</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">mass_scaling</span><span class="p">)</span>
-            <span class="c1"># Then the [throttles, tof]</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">mcg_th_tof</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">mass_scaling</span><span class="p">)</span>
-            <span class="n">retval</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">DAY2SEC</span>
-        <span class="c1"># 3 -  The gradient of the throttle constraints</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">nseg</span><span class="p">):</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">tcg_th</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">i</span> <span class="p">:</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">3</span><span class="p">])</span>
-
-        <span class="k">return</span> <span class="n">retval</span>
-
-    <span class="k">def</span> <span class="nf">gradient_sparsity</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="n">dim</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">3</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">nseg</span>
-        <span class="c1"># The objective function only depends on the final mass, which is in the chromosome.</span>
-        <span class="n">retval</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]]</span>
-        <span class="c1"># The mismatch constraints depend on all variables.</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">8</span><span class="p">):</span>
-            <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
-                <span class="n">retval</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">])</span>
-        <span class="c1"># The throttle constraints only depend on the specific throttles (3).</span>
-        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">nseg</span><span class="p">):</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="mi">8</span> <span class="o">+</span> <span class="n">i</span><span class="p">,</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="mi">8</span> <span class="o">+</span> <span class="n">i</span><span class="p">,</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span><span class="p">])</span>
-            <span class="n">retval</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="mi">8</span> <span class="o">+</span> <span class="n">i</span><span class="p">,</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">3</span><span class="p">])</span>
-        <span class="c1"># We return the sparsity pattern</span>
-        <span class="k">return</span> <span class="n">retval</span>
-
-    <span class="k">def</span> <span class="nf">get_nec</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="mi">7</span>
-
-    <span class="k">def</span> <span class="nf">get_nic</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
-        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="o">.</span><span class="n">nseg</span>
-
-    <span class="k">def</span> <span class="nf">pretty</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="sd">        Prints a detailed representation of the Point to point problem.</span>
-
-<span class="sd">        Args:</span>
-<span class="sd">            *x* (:class:`list`): The decision vector containing final mass, thrust direction, and time of flight.</span>
-<span class="sd">        &quot;&quot;&quot;</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">_set_leg_from_x</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-        <span class="nb">print</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">leg</span><span class="p">)</span>
-
-    <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span>
-        <span class="bp">self</span><span class="p">,</span>
-        <span class="n">x</span><span class="p">,</span>
-        <span class="n">ax</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
-        <span class="n">units</span><span class="o">=</span><span class="n">_pk</span><span class="o">.</span><span class="n">AU</span><span class="p">,</span>
-        <span class="n">show_midpoints</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
-        <span class="n">show_gridpoints</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
-        <span class="n">show_throttles</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
-        <span class="n">length</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span>
-        <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span>
-        <span class="o">**</span><span class="n">kwargs</span>
-    <span class="p">):</span>
-<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
-<span class="sd">        Plots the trajectory leg  3D axes.</span>
-
-<span class="sd">        Args:</span>
-<span class="sd">            *x* (:class:`list`): The decision vector containing final mass, thrust direction, and time of flight.</span>
-
-<span class="sd">            *ax* (:class:`mpl_toolkits.mplot3d.axes3d.Axes3D`, optional): The 3D axis to plot on. Defaults to None.</span>
-
-<span class="sd">            *units* (:class:`float`, optional): The unit scale for the plot. Defaults to _pk.AU.</span>
-
-<span class="sd">            *show_midpoints* (:class:`bool`, optional): Whether to show midpoints on the trajectory. Defaults to False.</span>
-
-<span class="sd">            *show_gridpoints* (:class:`bool`, optional): Whether to show grid points on the trajectory. Defaults to False.</span>
-
-<span class="sd">            *show_throttles* (:class:`bool`, optional): Whether to show throttle vectors. Defaults to False.</span>
-
-<span class="sd">            *length* (:class:`float`, optional): Length of the throttle vectors. Defaults to 0.1.</span>
-
-<span class="sd">            *arrow_length_ratio* (:class:`float`, optional): Arrow length ratio for the throttle vectors. Defaults to 0.05.</span>
-
-<span class="sd">            *\*\*kwargs*: Additional keyword arguments for the plot.</span>
-
-<span class="sd">        Returns:</span>
-<span class="sd">            :class:`mpl_toolkits.mplot3d.axes3d.Axes3D`: The 3D axis with the plotted trajectory.</span>
-<span class="sd">        &quot;&quot;&quot;</span>
-        <span class="bp">self</span><span class="o">.</span><span class="n">_set_leg_from_x</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
-        <span class="n">sf</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">leg</span>
-        <span class="c1"># Making the axis</span>
-        <span class="k">if</span> <span class="n">ax</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-            <span class="n">ax</span> <span class="o">=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">make_3Daxis</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">))</span>
-
-        <span class="n">rs</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">sf</span><span class="o">.</span><span class="n">rvs</span>
-        <span class="n">rf</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">sf</span><span class="o">.</span><span class="n">rvf</span>
-        <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">rs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">_pk</span><span class="o">.</span><span class="n">AU</span><span class="p">,</span> <span class="n">rs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="n">units</span><span class="p">,</span> <span class="n">rs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">/</span> <span class="n">units</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">&quot;k&quot;</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
-        <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">rf</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">_pk</span><span class="o">.</span><span class="n">AU</span><span class="p">,</span> <span class="n">rf</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="n">units</span><span class="p">,</span> <span class="n">rf</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">/</span> <span class="n">units</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">&quot;k&quot;</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
-
-        <span class="c1"># Plotting the trajctory leg</span>
-        <span class="n">ax</span> <span class="o">=</span> <span class="n">_pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">add_sf_leg</span><span class="p">(</span>
-            <span class="n">ax</span><span class="p">,</span>
-            <span class="n">sf</span><span class="p">,</span>
-            <span class="n">units</span><span class="o">=</span><span class="n">units</span><span class="p">,</span>
-            <span class="n">show_throttles</span><span class="o">=</span><span class="n">show_throttles</span><span class="p">,</span>
-            <span class="n">length</span><span class="o">=</span><span class="n">length</span><span class="p">,</span>
-            <span class="n">show_gridpoints</span><span class="o">=</span><span class="n">show_gridpoints</span><span class="p">,</span>
-            <span class="n">show_midpoints</span><span class="o">=</span><span class="n">show_midpoints</span><span class="p">,</span>
-            <span class="n">arrow_length_ratio</span><span class="o">=</span><span class="n">arrow_length_ratio</span><span class="p">,</span>
-            <span class="o">**</span><span class="n">kwargs</span>
-        <span class="p">)</span>
-
-        <span class="k">return</span> <span class="n">ax</span>
+<span class="p">)</span>
+
+<span class="n">udp_g</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">trajopt</span><span class="o">.</span><span class="n">direct_pl2pl</span><span class="p">(</span>
+        <span class="n">pls</span><span class="o">=</span><span class="n">earth</span><span class="p">,</span>
+        <span class="n">plf</span><span class="o">=</span><span class="n">mars</span><span class="p">,</span>
+        <span class="n">ms</span><span class="o">=</span><span class="n">ms</span><span class="p">,</span>
+        <span class="n">mu</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span><span class="p">,</span>
+        <span class="n">max_thrust</span><span class="o">=</span><span class="n">max_thrust</span><span class="p">,</span>
+        <span class="n">isp</span><span class="o">=</span><span class="mi">3000</span><span class="p">,</span>
+        <span class="n">t0_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">6700.0</span><span class="p">,</span> <span class="mf">6800.0</span><span class="p">],</span>
+        <span class="n">tof_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">200.0</span><span class="p">,</span> <span class="mf">300.0</span><span class="p">],</span>
+        <span class="n">mf_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">1300.</span><span class="p">,</span> <span class="n">ms</span><span class="p">],</span>
+        <span class="n">vinfs</span><span class="o">=</span><span class="mf">3.</span><span class="p">,</span>
+        <span class="n">vinff</span><span class="o">=</span><span class="mf">0.</span><span class="p">,</span>
+        <span class="n">nseg</span><span class="o">=</span><span class="n">nseg</span><span class="p">,</span>
+        <span class="n">cut</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span>
+        <span class="n">mass_scaling</span><span class="o">=</span><span class="n">ms</span><span class="p">,</span>
+        <span class="n">r_scaling</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">AU</span><span class="p">,</span>
+        <span class="n">v_scaling</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">EARTH_VELOCITY</span><span class="p">,</span>
+        <span class="n">with_gradient</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+<span class="p">)</span>
 </pre></div>
 </div>
 </div>
 </div>
+<section id="analytical-performances-of-the-analytical-gradient">
+<h2>Analytical performances of the analytical gradient<a class="headerlink" href="#analytical-performances-of-the-analytical-gradient" title="Permalink to this heading">#</a></h2>
+<p>And we take a quick look at the performances of the analytical gradient with respect to the numerically computed one.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Problem data</span>
-<span class="n">mu</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span>
-<span class="n">max_thrust</span> <span class="o">=</span> <span class="mf">0.12</span>
-<span class="n">isp</span> <span class="o">=</span> <span class="mi">3000</span>
-
-<span class="c1"># Initial state</span>
-<span class="n">ms</span> <span class="o">=</span> <span class="mf">1500.0</span>
-<span class="n">rs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.2</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.01</span><span class="p">])</span> <span class="o">*</span> <span class="n">pk</span><span class="o">.</span><span class="n">AU</span>
-<span class="n">vs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.01</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.01</span><span class="p">])</span> <span class="o">*</span> <span class="n">pk</span><span class="o">.</span><span class="n">EARTH_VELOCITY</span>
-
-<span class="c1"># Final state</span>
-<span class="n">mf</span> <span class="o">=</span> <span class="mf">1300.0</span>
-<span class="n">rf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0</span><span class="p">])</span> <span class="o">*</span> <span class="n">pk</span><span class="o">.</span><span class="n">AU</span>
-<span class="n">vf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.01</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0</span><span class="p">])</span> <span class="o">*</span> <span class="n">pk</span><span class="o">.</span><span class="n">EARTH_VELOCITY</span>
-
-<span class="c1"># Throttles and tof</span>
-<span class="n">nseg</span> <span class="o">=</span> <span class="mi">4</span>
-<span class="n">throttles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">nseg</span> <span class="o">*</span> <span class="mi">3</span><span class="p">))</span>
-<span class="n">tof</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">pk</span><span class="o">.</span><span class="n">AU</span><span class="o">**</span><span class="mi">3</span> <span class="o">/</span> <span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span><span class="p">)</span> <span class="o">/</span> <span class="mi">4</span>
-
-<span class="n">udp_nog</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">trajopt</span><span class="o">.</span><span class="n">direct_point2point</span><span class="p">(</span>
-    <span class="n">rvs</span><span class="o">=</span><span class="p">[</span><span class="n">rs</span><span class="p">,</span> <span class="n">vs</span><span class="p">],</span>
-    <span class="n">rvf</span><span class="o">=</span><span class="p">[</span><span class="n">rf</span><span class="p">,</span> <span class="n">vf</span><span class="p">],</span>
-    <span class="n">mu</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span><span class="p">,</span>
-    <span class="n">max_thrust</span><span class="o">=</span><span class="mf">0.22</span><span class="p">,</span>
-    <span class="n">isp</span><span class="o">=</span><span class="mi">3000</span><span class="p">,</span>
-    <span class="n">tof_bounds</span><span class="o">=</span><span class="p">[</span><span class="mi">200</span><span class="p">,</span> <span class="mi">500</span><span class="p">],</span>
-    <span class="n">mf_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">200.0</span><span class="p">,</span> <span class="mf">1000.0</span><span class="p">],</span>
-    <span class="n">nseg</span><span class="o">=</span><span class="n">nseg</span><span class="p">,</span>
-    <span class="n">cut</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span>
-    <span class="n">with_gradient</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
-<span class="p">)</span>
-
-<span class="n">udp_g</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">trajopt</span><span class="o">.</span><span class="n">direct_point2point</span><span class="p">(</span>
-    <span class="n">rvs</span><span class="o">=</span><span class="p">[</span><span class="n">rs</span><span class="p">,</span> <span class="n">vs</span><span class="p">],</span>
-    <span class="n">rvf</span><span class="o">=</span><span class="p">[</span><span class="n">rf</span><span class="p">,</span> <span class="n">vf</span><span class="p">],</span>
-    <span class="n">mu</span><span class="o">=</span><span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span><span class="p">,</span>
-    <span class="n">max_thrust</span><span class="o">=</span><span class="mf">0.22</span><span class="p">,</span>
-    <span class="n">isp</span><span class="o">=</span><span class="mi">3000</span><span class="p">,</span>
-    <span class="n">tof_bounds</span><span class="o">=</span><span class="p">[</span><span class="mi">200</span><span class="p">,</span> <span class="mi">500</span><span class="p">],</span>
-    <span class="n">mf_bounds</span><span class="o">=</span><span class="p">[</span><span class="mf">200.0</span><span class="p">,</span> <span class="mf">1000.0</span><span class="p">],</span>
-    <span class="n">nseg</span><span class="o">=</span><span class="n">nseg</span><span class="p">,</span>
-    <span class="n">cut</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span>
-    <span class="n">with_gradient</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
-<span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># We need to generste a random chromosomes compatible with the UDP where to test the gradient.</span>
+<span class="n">prob_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">problem</span><span class="p">(</span><span class="n">udp_g</span><span class="p">)</span>
+<span class="n">pop_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_g</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>First the analytical gradient:</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%%time</span>it
+<span class="n">udp_g</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">champion_x</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">line</span> <span class="mi">2</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Problem data</span>
-<span class="ne">----&gt; </span><span class="mi">2</span> <span class="n">mu</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">MU_SUN</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="n">max_thrust</span> <span class="o">=</span> <span class="mf">0.12</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="n">isp</span> <span class="o">=</span> <span class="mi">3000</span>
-
-<span class="ne">NameError</span>: name &#39;pk&#39; is not defined
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>268 μs ± 843 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
 </pre></div>
 </div>
 </div>
 </div>
+<p>Then a simple numerical gradient based on finite differences:</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">snopt72</span> <span class="o">=</span> <span class="s2">&quot;/usr/local/lib/libsnopt7_c.so&quot;</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%%time</span>it
+<span class="n">pg</span><span class="o">.</span><span class="n">estimate_gradient</span><span class="p">(</span><span class="n">udp_g</span><span class="o">.</span><span class="n">fitness</span><span class="p">,</span> <span class="n">pop_g</span><span class="o">.</span><span class="n">champion_x</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1.66 ms ± 283 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)
+</pre></div>
+</div>
+</div>
+</div>
+<p>Then a higher order numerical gradient:</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%%time</span>it
+<span class="n">pg</span><span class="o">.</span><span class="n">estimate_gradient_h</span><span class="p">(</span><span class="n">udp_g</span><span class="o">.</span><span class="n">fitness</span><span class="p">,</span> <span class="n">pop_g</span><span class="o">.</span><span class="n">champion_x</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>4.48 ms ± 374 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)
+</pre></div>
+</div>
+</div>
+</div>
+<p>The analytical gradient its exact and faster, seems like a no brainer to use it.</p>
+<p>In reality, the effects on the optimization technique used are not straightforward, making the option to use numerical gradients still interesting in some, albeit rare, cases.</p>
+</section>
+<section id="solving-the-low-thrust-transfer">
+<h2>Solving the low-thrust transfer<a class="headerlink" href="#solving-the-low-thrust-transfer" title="Permalink to this heading">#</a></h2>
+<p>We define (again) the optimization problem, and set a tolerance for <em>pagmo</em> to be able to judge the relative value of two individuals.</p>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>This tolerance has a different role from the numerical tolerance set in the particular algorithm chosen to solve the problem and is only used by the <em>pagmo</em> machinery to decide outside the optimizer whether the new proposed indivdual is better than what was the previous <em>champion</em>.</p>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">prob_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">problem</span><span class="p">(</span><span class="n">udp_g</span><span class="p">)</span>
+<span class="n">prob_g</span><span class="o">.</span><span class="n">c_tol</span> <span class="o">=</span> <span class="mf">1e-6</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>… and we define an optimization algorithm.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">snopt72</span> <span class="o">=</span> <span class="s2">&quot;/Users/dario.izzo/opt/libsnopt7_c.dylib&quot;</span>
 <span class="n">uda</span> <span class="o">=</span> <span class="n">ppnf</span><span class="o">.</span><span class="n">snopt7</span><span class="p">(</span><span class="n">library</span><span class="o">=</span><span class="n">snopt72</span><span class="p">,</span> <span class="n">minor_version</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">screen_output</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
 <span class="n">uda</span><span class="o">.</span><span class="n">set_integer_option</span><span class="p">(</span><span class="s2">&quot;Major iterations limit&quot;</span><span class="p">,</span> <span class="mi">2000</span><span class="p">)</span>
 <span class="n">uda</span><span class="o">.</span><span class="n">set_integer_option</span><span class="p">(</span><span class="s2">&quot;Iterations limit&quot;</span><span class="p">,</span> <span class="mi">20000</span><span class="p">)</span>
 <span class="n">uda</span><span class="o">.</span><span class="n">set_numeric_option</span><span class="p">(</span><span class="s2">&quot;Major optimality tolerance&quot;</span><span class="p">,</span> <span class="mf">1e-3</span><span class="p">)</span>
-<span class="n">uda</span><span class="o">.</span><span class="n">set_numeric_option</span><span class="p">(</span><span class="s2">&quot;Major feasibility tolerance&quot;</span><span class="p">,</span> <span class="mf">1e-12</span><span class="p">)</span>
+<span class="n">uda</span><span class="o">.</span><span class="n">set_numeric_option</span><span class="p">(</span><span class="s2">&quot;Major feasibility tolerance&quot;</span><span class="p">,</span> <span class="mf">1e-11</span><span class="p">)</span>
 
-<span class="c1"># uda = pg.nlopt(&quot;slsqp&quot;)</span>
+<span class="c1">#uda = pg.nlopt(&quot;slsqp&quot;)</span>
 <span class="n">algo</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">algorithm</span><span class="p">(</span><span class="n">uda</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 </div>
+<p>We solve the problem from random initial guess ten times and only save the result if a feasible solution is found (as defined by the criterias above)</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">prob_nog</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">problem</span><span class="p">(</span><span class="n">udp_nog</span><span class="p">)</span>
-<span class="n">prob_nog</span><span class="o">.</span><span class="n">c_tol</span> <span class="o">=</span> <span class="mf">1e-6</span>
-<span class="n">prob_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">problem</span><span class="p">(</span><span class="n">udp_g</span><span class="p">)</span>
-<span class="n">prob_g</span><span class="o">.</span><span class="n">c_tol</span> <span class="o">=</span> <span class="mf">1e-6</span>
-<span class="n">pop_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_g</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="n">pop_g</span> <span class="o">=</span> <span class="n">algo</span><span class="o">.</span><span class="n">evolve</span><span class="p">(</span><span class="n">pop_g</span><span class="p">)</span>
-<span class="nb">print</span><span class="p">(</span><span class="n">prob_g</span><span class="o">.</span><span class="n">feasibility_f</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">champion_f</span><span class="p">))</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">masses</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">xs</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
+    <span class="n">pop_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_g</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+    <span class="n">pop_g</span> <span class="o">=</span> <span class="n">algo</span><span class="o">.</span><span class="n">evolve</span><span class="p">(</span><span class="n">pop_g</span><span class="p">)</span>
+    <span class="k">if</span><span class="p">(</span><span class="n">prob_g</span><span class="o">.</span><span class="n">feasibility_f</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">champion_f</span><span class="p">)):</span>
+        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;.&quot;</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">&quot;&quot;</span><span class="p">)</span>
+        <span class="n">masses</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">champion_x</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+        <span class="n">xs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">champion_x</span><span class="p">)</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;x&quot;</span><span class="p">,</span> <span class="n">end</span> <span class="o">=</span><span class="s2">&quot;&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">Best mass is: &quot;</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">masses</span><span class="p">))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Worst mass is: &quot;</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">masses</span><span class="p">))</span>
+<span class="n">best_idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">masses</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>True
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span>---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Cell In[10], line 5
+      3 for i in range(10):
+      4     pop_g = pg.population(prob_g, 1)
+----&gt; 5     pop_g = algo.evolve(pop_g)
+      6     if(prob_g.feasibility_f(pop_g.champion_f)):
+      7         print(&quot;.&quot;, end=&quot;&quot;)
+
+ValueError: 
+function: evolve_version
+where: /home/conda/feedstock_root/build_artifacts/pygmo_plugins_nonfree_1712564791372/work/src/snopt7.cpp, 603
+what: 
+An error occurred while loading the snopt7_c library at run-time. This is typically caused by one of the following
+reasons:
+
+- The file declared to be the snopt7_c library, i.e. /Users/dario.izzo/opt/libsnopt7_c.dylib, is not a shared library containing the necessary C interface symbols (is the file path really pointing to
+a valid shared library?)
+ - The library is found and it does contain the C interface symbols, but it needs linking to some additional libraries that are not found
+at run-time.
+
+We report the exact text of the original exception thrown:
+
+ 
+function: evolve_version
+where: /home/conda/feedstock_root/build_artifacts/pygmo_plugins_nonfree_1712564791372/work/src/snopt7.cpp, 553
+what: The snopt7_c library path was constructed to be: /Users/dario.izzo/opt/libsnopt7_c.dylib and it does not appear to be a file
+
 </pre></div>
 </div>
 </div>
 </div>
+<p>And we plot the trajectory found:</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">ax</span> <span class="o">=</span> <span class="n">udp_nog</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">get_x</span><span class="p">()[</span><span class="mi">0</span><span class="p">],</span> <span class="n">show_gridpoints</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">ax</span> <span class="o">=</span> <span class="n">udp_g</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xs</span><span class="p">[</span><span class="n">best_idx</span><span class="p">],</span> <span class="n">show_gridpoints</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 <span class="n">ax</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="mi">90</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Mismatch on pos: [ 1.57696078e-12  1.61709535e-12 -1.75156764e-13]
-Mismatch on mass: 4.126786734559573e-08
-</pre></div>
-</div>
-<img alt="../_images/c7580ac5663c46303460d6f091cc21b73bc5411a08410629a341127cd023ae44.png" src="../_images/c7580ac5663c46303460d6f091cc21b73bc5411a08410629a341127cd023ae44.png" />
+<img alt="../_images/3dae57626a3b567cad10e9de720686602dd4cc325f35023bee1f01b70102c20e.png" src="../_images/3dae57626a3b567cad10e9de720686602dd4cc325f35023bee1f01b70102c20e.png" />
 </div>
 </div>
+</section>
+<section id="graident-vs-no-gradient">
+<h2>Graident vs no gradient<a class="headerlink" href="#graident-vs-no-gradient" title="Permalink to this heading">#</a></h2>
+<p>We here take a look at the difference in solving the problem using the analytical gradient and not using it.
+To do so we solve the same problem starting from 100 different initial guesses using both versions and compare.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">tqdm</span> <span class="kn">import</span> <span class="n">tqdm</span>
@@ -840,25 +701,31 @@ <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-p
 <span class="n">fail_g</span> <span class="o">=</span> <span class="mi">0</span>
 <span class="n">fail_nog</span> <span class="o">=</span> <span class="mi">0</span>
 
-<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">tqdm</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">2000</span><span class="p">)):</span>
-    <span class="n">pop_nog</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_nog</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="n">prob_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">problem</span><span class="p">(</span><span class="n">udp_g</span><span class="p">)</span>
+<span class="n">prob_nog</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">problem</span><span class="p">(</span><span class="n">udp_nog</span><span class="p">)</span>
+<span class="n">prob_g</span><span class="o">.</span><span class="n">c_tol</span> <span class="o">=</span> <span class="mf">1e-6</span>
+<span class="n">prob_nog</span><span class="o">.</span><span class="n">c_tol</span> <span class="o">=</span> <span class="mf">1e-6</span>
 
-    <span class="n">pop_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_g</span><span class="p">)</span>
-    <span class="n">pop_g</span><span class="o">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pop_nog</span><span class="o">.</span><span class="n">get_x</span><span class="p">()[</span><span class="mi">0</span><span class="p">])</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">tqdm</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">)):</span>
+    <span class="n">pop_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_g</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+    <span class="n">pop_nog</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_nog</span><span class="p">)</span>
+    <span class="n">pop_nog</span><span class="o">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">champion_x</span><span class="p">)</span>
 
     <span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
     <span class="n">pop_g</span> <span class="o">=</span> <span class="n">algo</span><span class="o">.</span><span class="n">evolve</span><span class="p">(</span><span class="n">pop_g</span><span class="p">)</span>
     <span class="n">end</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
-    <span class="n">cpu_g</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">end</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span>
     <span class="k">if</span> <span class="ow">not</span> <span class="n">prob_g</span><span class="o">.</span><span class="n">feasibility_f</span><span class="p">(</span><span class="n">pop_g</span><span class="o">.</span><span class="n">champion_f</span><span class="p">):</span>
         <span class="n">fail_g</span> <span class="o">+=</span> <span class="mi">1</span>
+    <span class="k">else</span><span class="p">:</span> <span class="c1"># We only record the time for successfull attempts</span>
+        <span class="n">cpu_g</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">end</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span>
 
     <span class="n">start</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
     <span class="n">pop_nog</span> <span class="o">=</span> <span class="n">algo</span><span class="o">.</span><span class="n">evolve</span><span class="p">(</span><span class="n">pop_nog</span><span class="p">)</span>
     <span class="n">end</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
-    <span class="n">cpu_nog</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">end</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span>
     <span class="k">if</span> <span class="ow">not</span> <span class="n">prob_nog</span><span class="o">.</span><span class="n">feasibility_f</span><span class="p">(</span><span class="n">pop_nog</span><span class="o">.</span><span class="n">champion_f</span><span class="p">):</span>
         <span class="n">fail_nog</span> <span class="o">+=</span> <span class="mi">1</span>
+    <span class="k">else</span><span class="p">:</span> <span class="c1"># We only record the time for successfull attempts</span>
+        <span class="n">cpu_nog</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">end</span> <span class="o">-</span> <span class="n">start</span><span class="p">)</span>
 
 <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Gradient: </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">cpu_g</span><span class="p">)</span><span class="si">:</span><span class="s2">.4e</span><span class="si">}</span><span class="s2">s&quot;</span><span class="p">)</span>
 <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;No Gradient: </span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">median</span><span class="p">(</span><span class="n">cpu_nog</span><span class="p">)</span><span class="si">:</span><span class="s2">.4e</span><span class="si">}</span><span class="s2">s&quot;</span><span class="p">)</span>
@@ -869,13 +736,14 @@ <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-p
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|██████████| 2000/2000 [02:18&lt;00:00, 14.45it/s]
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|██████████| 100/100 [02:09&lt;00:00,  1.29s/it]
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Gradient: 1.8443e-02s
-No Gradient: 3.0552e-02s
-Gradient: 192
-No Gradient: 188
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Gradient: 4.8809e-01s
+No Gradient: 5.5510e-01s
+
+Gradient (n.fails): 7
+No Gradient (n.fails): 64
 </pre></div>
 </div>
 <div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
@@ -887,8 +755,8 @@ <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-p
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">cpu_g</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cpu_g</span><span class="p">)</span>
 <span class="n">cpu_nog</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cpu_nog</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">cpu_g</span><span class="p">[</span><span class="n">cpu_g</span> <span class="o">&lt;</span> <span class="mf">0.2</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;gradient&quot;</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">cpu_nog</span><span class="p">[</span><span class="n">cpu_nog</span> <span class="o">&lt;</span> <span class="mf">0.2</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;no_gradient&quot;</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">cpu_g</span><span class="p">[</span><span class="n">cpu_g</span> <span class="o">&lt;</span> <span class="mf">2.2</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;gradient&quot;</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">cpu_nog</span><span class="p">[</span><span class="n">cpu_nog</span> <span class="o">&lt;</span> <span class="mf">1.2</span><span class="p">],</span> <span class="n">bins</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;no_gradient&quot;</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
 <span class="c1"># plt.xlim([0,0.15])</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;point2point, 4 seg case&quot;</span><span class="p">)</span>
@@ -898,9 +766,13 @@ <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-p
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/7b80001d91b87326c24c871092a270c632c04265556c4454fefb4ae4d4182f6c.png" src="../_images/7b80001d91b87326c24c871092a270c632c04265556c4454fefb4ae4d4182f6c.png" />
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;N. occurrences&#39;)
+</pre></div>
 </div>
+<img alt="../_images/cfe10624ec001205eb75198db6126ff26b314565b0abd800cd2efc1843999535.png" src="../_images/cfe10624ec001205eb75198db6126ff26b314565b0abd800cd2efc1843999535.png" />
 </div>
+</div>
+</section>
 </section>
 
 
@@ -921,6 +793,23 @@ <h1>Planet to planet low-thrust transfer<a class="headerlink" href="#planet-to-p
             
             
               
+                <div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
+
+
+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#analytical-performances-of-the-analytical-gradient">Analytical performances of the analytical gradient</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-the-low-thrust-transfer">Solving the low-thrust transfer</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#graident-vs-no-gradient">Graident vs no gradient</a></li>
+</ul>
+  </nav></div>
+
+</div></div>
+              
             
           </div>
           <footer class="bd-footer-content">
diff --git a/notebooks/udp_point2point.html b/notebooks/udp_point2point.html
index a1b3de4..fcc339a 100644
--- a/notebooks/udp_point2point.html
+++ b/notebooks/udp_point2point.html
@@ -501,7 +501,7 @@ <h1>Point to point low-thrust transfer<a class="headerlink" href="#point-to-poin
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">snopt72</span> <span class="o">=</span> <span class="s2">&quot;/usr/local/lib/libsnopt7_c.so&quot;</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">snopt72</span> <span class="o">=</span> <span class="s2">&quot;/Users/dario.izzo/opt/libsnopt7_c.dylib&quot;</span>
 <span class="n">uda</span> <span class="o">=</span> <span class="n">ppnf</span><span class="o">.</span><span class="n">snopt7</span><span class="p">(</span><span class="n">library</span><span class="o">=</span><span class="n">snopt72</span><span class="p">,</span> <span class="n">minor_version</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">screen_output</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
 <span class="n">uda</span><span class="o">.</span><span class="n">set_integer_option</span><span class="p">(</span><span class="s2">&quot;Major iterations limit&quot;</span><span class="p">,</span> <span class="mi">2000</span><span class="p">)</span>
 <span class="n">uda</span><span class="o">.</span><span class="n">set_integer_option</span><span class="p">(</span><span class="s2">&quot;Iterations limit&quot;</span><span class="p">,</span> <span class="mi">20000</span><span class="p">)</span>
@@ -540,7 +540,7 @@ <h1>Point to point low-thrust transfer<a class="headerlink" href="#point-to-poin
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/0293889e5651601087e2954b9b15faa5a96edaa9c0d71dc99ac4336d58cc6488.png" src="../_images/0293889e5651601087e2954b9b15faa5a96edaa9c0d71dc99ac4336d58cc6488.png" />
+<img alt="../_images/42008612a1329165223a9fd1794d68c90873a5096831157c380fcab7c024af13.png" src="../_images/42008612a1329165223a9fd1794d68c90873a5096831157c380fcab7c024af13.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -582,19 +582,17 @@ <h1>Point to point low-thrust transfer<a class="headerlink" href="#point-to-poin
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>  0%|          | 0/2000 [00:00&lt;?, ?it/s]
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|██████████| 2000/2000 [04:06&lt;00:00,  8.13it/s]
 </pre></div>
 </div>
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">line</span> <span class="mi">10</span>
-<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="n">fail_nog</span> <span class="o">=</span> <span class="mi">0</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">tqdm</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">2000</span><span class="p">)):</span>
-<span class="ne">---&gt; </span><span class="mi">10</span>     <span class="n">pop_nog</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_nog</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">12</span>     <span class="n">pop_g</span> <span class="o">=</span> <span class="n">pg</span><span class="o">.</span><span class="n">population</span><span class="p">(</span><span class="n">prob_g</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">13</span>     <span class="n">pop_g</span><span class="o">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pop_nog</span><span class="o">.</span><span class="n">get_x</span><span class="p">()[</span><span class="mi">0</span><span class="p">])</span>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Gradient: 5.6576e-02s
+No Gradient: 5.9454e-02s
 
-<span class="ne">NameError</span>: name &#39;pg&#39; is not defined
+Gradient (n.fails): 208
+No Gradient (n.fails): 206
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
 </pre></div>
 </div>
 </div>
@@ -614,7 +612,10 @@ <h1>Point to point low-thrust transfer<a class="headerlink" href="#point-to-poin
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/7b80001d91b87326c24c871092a270c632c04265556c4454fefb4ae4d4182f6c.png" src="../_images/7b80001d91b87326c24c871092a270c632c04265556c4454fefb4ae4d4182f6c.png" />
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0, 0.5, &#39;N. occurrences&#39;)
+</pre></div>
+</div>
+<img alt="../_images/7243bfe4087b822870d5a18726e2015d293585820184dceef5d55a768a49f971.png" src="../_images/7243bfe4087b822870d5a18726e2015d293585820184dceef5d55a768a49f971.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -625,9 +626,9 @@ <h1>Point to point low-thrust transfer<a class="headerlink" href="#point-to-poin
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Number of segments: 4
-Number of fwd segments: 2
-Number of bck segments: 2
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Number of segments: 2
+Number of fwd segments: 1
+Number of bck segments: 1
 Maximum thrust: 0.22
 Central body gravitational parameter: 1.32712440018e+20
 Specific impulse: 3000
@@ -637,10 +638,10 @@ <h1>Point to point low-thrust transfer<a class="headerlink" href="#point-to-poin
 Final mass: 1
 State at departure: [[179517444840, 0, -1495978707], [297.8469183169681, 29784.691831696804, -297.8469183169681]]
 State at arrival: [[149597870700, 0, -0], [297.8469183169681, 32763.161014866488, -0]]
-Throttles values: [-0.5531180194281187, 0.14971757884060444, 0.7940199350920427, 0.028288032565428445, -0.11046018798817858, -0.800424150704127, -0.6581747271243201, -0.5884590126432687, 0.9303693454363375, -0.7082653660632694, 0.3855806880092745, 0.3899050835184499]
+Throttles values: [0, 0, 0, 0, 0, 0]
 
-Mismatch constraints: [29919970440.50476, 38523538.099015325, -1496184052.1450462, -98.7230576541013, -2992.131264375472, -208.49434302739866, 998.99085894998]
-Throttle constraints: [-0.04117744584645111, -0.34631951305277053, 0.6450650999139032, -0.19766173011602817]
+Mismatch constraints: [29919941431.26764, 38529477.27626525, -1496162174.1910896, -6.189427009557562, -2978.469066381742, -297.82577960576987, 999]
+Throttle constraints: [-1, -1]
 </pre></div>
 </div>
 </div>
diff --git a/objects.inv b/objects.inv
index 4df6d4b..9fb3113 100644
Binary files a/objects.inv and b/objects.inv differ
diff --git a/plot.html b/plot.html
index c299b62..af8224b 100644
--- a/plot.html
+++ b/plot.html
@@ -423,7 +423,7 @@ <h2>Common utils<a class="headerlink" href="#common-utils" title="Permalink to t
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">make_3Daxis</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.make_3Daxis" title="Permalink to this definition">#</a></dt>
 <dd><p>Constructs and returns a 3D axis.  All kwargs are forwarded to the call to <cite>figure()</cite> in matplotlib.</p>
 <dl class="simple">
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis</p>
 </dd>
 </dl>
 </dd></dl>
@@ -436,9 +436,9 @@ <h2>Plotting planets<a class="headerlink" href="#plotting-planets" title="Permal
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">add_sun</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ax</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.add_sun" title="Permalink to this definition">#</a></dt>
 <dd><p>Adds the Sun to <em>ax</em>. All kwargs are forwarded to the scatter method of <em>ax</em>.</p>
 <dl class="simple">
-<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
+<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
 </dd>
 </dl>
 </dd></dl>
@@ -448,12 +448,12 @@ <h2>Plotting planets<a class="headerlink" href="#plotting-planets" title="Permal
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">add_planet</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ax</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pla</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="planet.html#pykep.planet" title="pykep.core.planet"><span class="pre">planet</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">when</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">units</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">149597870700.0</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.add_planet" title="Permalink to this definition">#</a></dt>
 <dd><p>Adds a planet to <em>ax</em>.  All kwargs are forwarded to the scatter method of <em>ax</em>.</p>
 <dl>
-<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
+<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
 <p><em>pla</em> (<a class="reference internal" href="planet.html#pykep.planet" title="pykep.planet"><code class="xref py py-class docutils literal notranslate"><span class="pre">planet</span></code></a>): the planet.</p>
 <p><em>when</em> (<a class="reference internal" href="epoch.html#pykep.epoch" title="pykep.epoch"><code class="xref py py-class docutils literal notranslate"><span class="pre">epoch</span></code></a> or <a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): the epoch (in mjd2000 if float).</p>
 <p><em>units</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): length units to be used. Defaults to pk.AU.</p>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
 </dd>
 <dt>Examples:</dt><dd><div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">pykep</span> <span class="k">as</span> <span class="nn">pk</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">ax</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">make_3Daxis</span><span class="p">()</span>
@@ -473,12 +473,12 @@ <h2>Plotting planets<a class="headerlink" href="#plotting-planets" title="Permal
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">add_planet_orbit</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ax</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pla</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="planet.html#pykep.planet" title="pykep.core.planet"><span class="pre">planet</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_range</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">units</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">149597870700.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">60</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.add_planet_orbit" title="Permalink to this definition">#</a></dt>
 <dd><p>Adds a planet orbit to <em>ax</em>. All kwargs are forwarded to the plot method of <em>ax</em>.</p>
 <dl>
-<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
+<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
 <p><em>pla</em> (<a class="reference internal" href="planet.html#pykep.planet" title="pykep.planet"><code class="xref py py-class docutils literal notranslate"><span class="pre">planet</span></code></a>): the planet.</p>
 <p><em>plot_range</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>, optional): the starting and end mjd2000 to be plotted. Defaults to [0., one_orbital_period] if a period can be computed.</p>
 <p><em>units</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): length units to be used. Defaults to pk.AU.</p>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
 </dd>
 <dt>Examples:</dt><dd><div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">pykep</span> <span class="k">as</span> <span class="nn">pk</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">ax</span> <span class="o">=</span> <span class="n">pk</span><span class="o">.</span><span class="n">plot</span><span class="o">.</span><span class="n">make_3Daxis</span><span class="p">()</span>
@@ -498,12 +498,12 @@ <h2>Plotting planets<a class="headerlink" href="#plotting-planets" title="Permal
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">add_solar_system</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="pre">ax,</span> <span class="pre">bodies=[1,</span> <span class="pre">2,</span> <span class="pre">3,</span> <span class="pre">4,</span> <span class="pre">5,</span> <span class="pre">6],</span> <span class="pre">ep=2000-01-01T00:00:00.000000,</span> <span class="pre">s=[15,</span> <span class="pre">2,</span> <span class="pre">3,</span> <span class="pre">3,</span> <span class="pre">2,</span> <span class="pre">8,</span> <span class="pre">8,</span> <span class="pre">5,</span> <span class="pre">5]</span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.add_solar_system" title="Permalink to this definition">#</a></dt>
 <dd><p>Adds to <em>ax</em> the selected solar system planets.</p>
 <dl>
-<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
+<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): the 3D axis.</p>
 <p><em>bodies</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>, optional): the solar system planet id (i.e. 3 for Earth). Defaults to [1, 2, 3, 4, 5, 6].</p>
 <p><em>ep</em> (<a class="reference internal" href="epoch.html#pykep.epoch" title="pykep.epoch"><code class="xref py py-class docutils literal notranslate"><span class="pre">epoch</span></code></a>): the epoch.</p>
 <p><em>s</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>, optional): the size of the Sun and all the 8 solar system planets. Defaults to [15, 2, 3, 3, 2, 8, 8, 5, 5].</p>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: the 3D axis.</p>
 </dd>
 </dl>
 </dd></dl>
@@ -516,7 +516,7 @@ <h2>Plotting trajectories<a class="headerlink" href="#plotting-trajectories" tit
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">add_lambert</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ax</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><span class="pre">int</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">60</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sol</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><span class="pre">int</span></a></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">units</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">149597870700.0</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.add_lambert" title="Permalink to this definition">#</a></dt>
 <dd><p>Add Lambert’s problem solution trajectory to a 3D matplotlib Axes.</p>
 <dl>
-<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): The 3D Axes object to which the trajectory will be added.</p>
+<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): The 3D Axes object to which the trajectory will be added.</p>
 <p><em>lp</em> (<a class="reference internal" href="lambert.html#pykep.lambert_problem" title="pykep.lambert_problem"><code class="xref py py-class docutils literal notranslate"><span class="pre">lambert_problem</span></code></a>): The Lambert’s problem object containing relevant information.</p>
 <p><em>N</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, optional): The number of points to generate along the trajectory. Default is 60.</p>
 <p><em>sol</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, optional): The solution index for Lambert’s problem. Default is 0.</p>
@@ -530,7 +530,7 @@ <h2>Plotting trajectories<a class="headerlink" href="#plotting-trajectories" tit
 The integration grid is defined based on the specified solution index and angle computations.
 The resulting trajectory is plotted on the given Axes object using the provided unit conversion factor.</p>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The modified Axes object with the Lambert’s problem trajectory added.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The modified Axes object with the Lambert’s problem trajectory added.</p>
 </dd>
 </dl>
 </dd></dl>
@@ -540,7 +540,7 @@ <h2>Plotting trajectories<a class="headerlink" href="#plotting-trajectories" tit
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">add_ballistic_arc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ax</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rv0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tof</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">units</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">149597870700.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">60</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.add_ballistic_arc" title="Permalink to this definition">#</a></dt>
 <dd><p>Add a ballistic trajectory arc to a 3D matplotlib Axes.</p>
 <dl>
-<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): The 3D Axes object to which the ballistic arc will be added.</p>
+<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): The 3D Axes object to which the ballistic arc will be added.</p>
 <p><em>rv0</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): Initial position and velocity vector in Cartesian coordinates.</p>
 <p><em>tof</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Time of flight for the ballistic arc.</p>
 <p><em>mu</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Gravitational parameter of the central body.</p>
@@ -554,7 +554,7 @@ <h2>Plotting trajectories<a class="headerlink" href="#plotting-trajectories" tit
 <li><p>The resulting trajectory is plotted on the given Axes object using the provided unit conversion factor.</p></li>
 </ul>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The modified Axes object with the ballistic arc trajectory added.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The modified Axes object with the ballistic arc trajectory added.</p>
 </dd>
 </dl>
 </dd></dl>
@@ -564,7 +564,7 @@ <h2>Plotting trajectories<a class="headerlink" href="#plotting-trajectories" tit
 <span class="sig-prename descclassname"><span class="pre">pykep.plot.</span></span><span class="sig-name descname"><span class="pre">add_sf_leg</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ax</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sf</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="leg.html#pykep.leg.sims_flanagan" title="leg._sims_flanagan"><span class="pre">_sims_flanagan</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">units</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">149597870700.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_midpoints</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_gridpoints</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_throttles</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">arrow_length_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.05</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.plot.add_sf_leg" title="Permalink to this definition">#</a></dt>
 <dd><p>Add a trajectory leg of Sims-Flanagan problem to a 3D matplotlib Axes.</p>
 <dl>
-<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): The 3D Axes object to which the trajectory leg will be added.</p>
+<dt>Args:</dt><dd><p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>): The 3D Axes object to which the trajectory leg will be added.</p>
 <p><em>sf</em> (<a class="reference internal" href="leg.html#pykep.leg.sims_flanagan" title="pykep.leg.sims_flanagan"><code class="xref py py-class docutils literal notranslate"><span class="pre">sims_flanagan</span></code></a>): The Sims-Flanagan object containing relevant information.</p>
 <p><em>units</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): The unit conversion factor for plotting. Default is pk.AU.</p>
 <p><em>N</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, optional): The number of points to generate along each segment of the trajectory. Default is 10.</p>
@@ -580,7 +580,7 @@ <h2>Plotting trajectories<a class="headerlink" href="#plotting-trajectories" tit
 <li><p>Midpoints, gridpoints, and thrust vectors can be optionally shown based on the provided parameters.</p></li>
 </ul>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The modified Axes object with the Sims-Flanagan leg added.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The modified Axes object with the Sims-Flanagan leg added.</p>
 </dd>
 </dl>
 </dd></dl>
diff --git a/reports/notebooks/plotting.err.log b/reports/notebooks/plotting.err.log
new file mode 100644
index 0000000..10b239a
--- /dev/null
+++ b/reports/notebooks/plotting.err.log
@@ -0,0 +1,51 @@
+Traceback (most recent call last):
+  File "/home/runner/local/lib/python3.11/site-packages/jupyter_cache/executors/utils.py", line 58, in single_nb_execution
+    executenb(
+  File "/home/runner/local/lib/python3.11/site-packages/nbclient/client.py", line 1314, in execute
+    return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
+           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+  File "/home/runner/local/lib/python3.11/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
+    return loop.run_until_complete(inner)
+           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+  File "/home/runner/local/lib/python3.11/asyncio/base_events.py", line 654, in run_until_complete
+    return future.result()
+           ^^^^^^^^^^^^^^^
+  File "/home/runner/local/lib/python3.11/site-packages/nbclient/client.py", line 709, in async_execute
+    await self.async_execute_cell(
+  File "/home/runner/local/lib/python3.11/site-packages/nbclient/client.py", line 1062, in async_execute_cell
+    await self._check_raise_for_error(cell, cell_index, exec_reply)
+  File "/home/runner/local/lib/python3.11/site-packages/nbclient/client.py", line 918, in _check_raise_for_error
+    raise CellExecutionError.from_cell_and_msg(cell, exec_reply_content)
+nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell:
+------------------
+ax = pk.plot.make_3Daxis(figsize = (6,6))
+ep = pk.epoch(0)
+pk.plot.add_solar_system(ax, bodies = [1,2,3,4,5], ep = ep)
+ax.view_init(90,0)
+ax.legend()
+ax.axis('off')
+ax.set_xlim3d(-4,4)
+ax.set_ylim3d(-4,4)
+ax.view_init(90,0)
+ax.set_title("The solar system up to Jupiter at mjd2000=0.");
+------------------
+
+
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Cell In[4], line 3
+      1 ax = pk.plot.make_3Daxis(figsize = (6,6))
+      2 ep = pk.epoch(0)
+----> 3 pk.plot.add_solar_system(ax, bodies = [1,2,3,4,5], ep = ep)
+      4 ax.view_init(90,0)
+      5 ax.legend()
+
+File ~/local/lib/python3.11/site-packages/pykep/plot/_planet.py:117, in add_solar_system(ax, bodies, ep, s)
+    115 if 1 in bodies:
+    116     udpla = _pk.udpla.jpl_lp(body="Mercury")
+--> 117     mercury = _pk.planet_to_keplerian(_pk.planet(udpla), ep=ep)
+    118     _pk.plot.add_planet_orbit(ax, mercury, c="tomato", label="")
+    119     _pk.plot.add_planet(ax, mercury, when=ep, c="tomato", s=s[1], label = "Mercury")
+
+TypeError: planet_to_keplerian() got an unexpected keyword argument 'ep'
+
diff --git a/reports/notebooks/udp_pl2pl.err.log b/reports/notebooks/udp_pl2pl.err.log
index f171c3b..e62880a 100644
--- a/reports/notebooks/udp_pl2pl.err.log
+++ b/reports/notebooks/udp_pl2pl.err.log
@@ -18,61 +18,50 @@ Traceback (most recent call last):
     raise CellExecutionError.from_cell_and_msg(cell, exec_reply_content)
 nbclient.exceptions.CellExecutionError: An error occurred while executing the following cell:
 ------------------
-# Problem data
-mu = pk.MU_SUN
-max_thrust = 0.12
-isp = 3000
+masses = []
+xs = []
+for i in range(10):
+    pop_g = pg.population(prob_g, 1)
+    pop_g = algo.evolve(pop_g)
+    if(prob_g.feasibility_f(pop_g.champion_f)):
+        print(".", end="")
+        masses.append(pop_g.champion_x[1])
+        xs.append(pop_g.champion_x)
+    else:
+        print("x", end ="")
+print("\nBest mass is: ", np.max(masses))
+print("Worst mass is: ", np.min(masses))
+best_idx = np.argmax(masses)
+------------------
 
-# Initial state
-ms = 1500.0
-rs = np.array([1.2, 0.0, -0.01]) * pk.AU
-vs = np.array([0.01, 1, -0.01]) * pk.EARTH_VELOCITY
 
-# Final state
-mf = 1300.0
-rf = np.array([1, 0.0, -0.0]) * pk.AU
-vf = np.array([0.01, 1.1, -0.0]) * pk.EARTH_VELOCITY
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Cell In[10], line 5
+      3 for i in range(10):
+      4     pop_g = pg.population(prob_g, 1)
+----> 5     pop_g = algo.evolve(pop_g)
+      6     if(prob_g.feasibility_f(pop_g.champion_f)):
+      7         print(".", end="")
 
-# Throttles and tof
-nseg = 4
-throttles = np.random.uniform(-1, 1, size=(nseg * 3))
-tof = 2 * np.pi * np.sqrt(pk.AU**3 / pk.MU_SUN) / 4
+ValueError: 
+function: evolve_version
+where: /home/conda/feedstock_root/build_artifacts/pygmo_plugins_nonfree_1712564791372/work/src/snopt7.cpp, 603
+what: 
+An error occurred while loading the snopt7_c library at run-time. This is typically caused by one of the following
+reasons:
 
-udp_nog = pk.trajopt.direct_point2point(
-    rvs=[rs, vs],
-    rvf=[rf, vf],
-    mu=pk.MU_SUN,
-    max_thrust=0.22,
-    isp=3000,
-    tof_bounds=[200, 500],
-    mf_bounds=[200.0, 1000.0],
-    nseg=nseg,
-    cut=0.6,
-    with_gradient=False,
-)
+- The file declared to be the snopt7_c library, i.e. /Users/dario.izzo/opt/libsnopt7_c.dylib, is not a shared library containing the necessary C interface symbols (is the file path really pointing to
+a valid shared library?)
+ - The library is found and it does contain the C interface symbols, but it needs linking to some additional libraries that are not found
+at run-time.
 
-udp_g = pk.trajopt.direct_point2point(
-    rvs=[rs, vs],
-    rvf=[rf, vf],
-    mu=pk.MU_SUN,
-    max_thrust=0.22,
-    isp=3000,
-    tof_bounds=[200, 500],
-    mf_bounds=[200.0, 1000.0],
-    nseg=nseg,
-    cut=0.6,
-    with_gradient=True,
-)
-------------------
+We report the exact text of the original exception thrown:
 
+ 
+function: evolve_version
+where: /home/conda/feedstock_root/build_artifacts/pygmo_plugins_nonfree_1712564791372/work/src/snopt7.cpp, 553
+what: The snopt7_c library path was constructed to be: /Users/dario.izzo/opt/libsnopt7_c.dylib and it does not appear to be a file
 
----------------------------------------------------------------------------
-NameError                                 Traceback (most recent call last)
-Cell In[3], line 2
-      1 # Problem data
-----> 2 mu = pk.MU_SUN
-      3 max_thrust = 0.12
-      4 isp = 3000
 
-NameError: name 'pk' is not defined
 
diff --git a/searchindex.js b/searchindex.js
index e673c89..a448033 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"docnames": ["anomalies", "api", "bibliography", "constants", "elements", "epoch", "index", "lambert", "leg", "notebooks/anomalies", "notebooks/epochs", "notebooks/interface_to_spice", "notebooks/planet", "notebooks/plotting", "notebooks/propagate_lagrangian", "notebooks/sims_flanagan_leg", "notebooks/udp_pl2pl", "notebooks/udp_point2point", "planet", "plot", "propagation", "trajopt", "tut_basic", "tut_trajopt", "udpla"], "filenames": ["anomalies.rst", "api.rst", "bibliography.rst", "constants.rst", "elements.rst", "epoch.rst", "index.md", "lambert.rst", "leg.rst", "notebooks/anomalies.ipynb", "notebooks/epochs.ipynb", "notebooks/interface_to_spice.ipynb", "notebooks/planet.ipynb", "notebooks/plotting.ipynb", "notebooks/propagate_lagrangian.ipynb", "notebooks/sims_flanagan_leg.ipynb", "notebooks/udp_pl2pl.ipynb", "notebooks/udp_point2point.ipynb", "planet.rst", "plot.rst", "propagation.rst", "trajopt.rst", "tut_basic.rst", "tut_trajopt.rst", "udpla.rst"], "titles": ["Anomalies Conversions", "API", "Bibliography", "Global constants", "Orbital Elements", "Epoch class", "Welcome to pykep\u2019s documentation!", "Lambert class", "Interplanetary transfer legs", "The various anomalies in pykep", "Epochs and Julian Dates", "Interfacing to SPICE and JPL DE ephs", "Ephemerides", "Plotting", "Lagrange Propagation", "The Sims-Flanagan trajectory leg", "Planet to planet low-thrust transfer", "Point to point low-thrust transfer", "Planet class", "The plot module", "Numerical Propagation", "Trajectory Optimization", "Basic", "Trajectory Optimization", "List of user implemented planets (UDPLAs)"], "terms": {"In": [0, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21], "pykep": [0, 1, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], "we": [0, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20], "adopt": 0, "follow": [0, 8, 10, 11, 12, 14, 18], "name": [0, 3, 9, 11, 12, 16, 17, 18, 24], "variou": [0, 3, 4, 6, 12, 13, 22], "m": [0, 3, 4, 6, 8, 9, 11, 14, 15, 16, 17, 18, 21], "i": [0, 1, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24], "mean": [0, 4, 9, 10, 12, 16, 24], "e": [0, 4, 8, 9, 10, 15, 18, 19, 24], "eccentr": [0, 9, 12, 14], "l": [0, 4, 9, 14], "true": [0, 4, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24], "longitud": [0, 4, 9], "lambda": [0, 9], "h": [0, 2, 4, 9], "hyperbol": [0, 9, 14], "n": [0, 2, 3, 9, 13, 14, 15, 16, 17, 19, 21], "zeta": [0, 9], "gudermannian": [0, 9], "function": [0, 3, 4, 9, 10, 11, 14, 16, 18, 19, 24], "variabl": [0, 7, 9, 16], "symbol": [0, 3, 9], "can": [0, 3, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24], "spell": [0, 14], "out": [0, 14], "like": [0, 7, 8, 10, 20, 24], "made": [0, 7, 11, 12], "lowercas": 0, "below": [0, 13, 14], "list": [0, 1, 6, 8, 11, 16, 18, 19, 20, 21], "allow": [0, 6, 7, 8, 10, 12, 14, 16, 18, 20], "convert": [0, 4, 9, 10, 11], "from": [0, 4, 5, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 24], "one": [0, 3, 5, 10, 11, 13, 14, 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\ No newline at end of file
+Search.setIndex({"docnames": ["anomalies", "api", "bibliography", "constants", "elements", "epoch", "index", "lambert", "leg", "notebooks/anomalies", "notebooks/epochs", "notebooks/interface_to_spice", "notebooks/planet", "notebooks/plotting", "notebooks/propagate_lagrangian", "notebooks/sims_flanagan_leg", "notebooks/udp_pl2pl", "notebooks/udp_point2point", "planet", "plot", "propagation", "trajopt", "tut_basic", "tut_trajopt", "udpla"], "filenames": ["anomalies.rst", "api.rst", "bibliography.rst", "constants.rst", "elements.rst", "epoch.rst", "index.md", "lambert.rst", "leg.rst", "notebooks/anomalies.ipynb", "notebooks/epochs.ipynb", "notebooks/interface_to_spice.ipynb", "notebooks/planet.ipynb", "notebooks/plotting.ipynb", "notebooks/propagate_lagrangian.ipynb", "notebooks/sims_flanagan_leg.ipynb", "notebooks/udp_pl2pl.ipynb", "notebooks/udp_point2point.ipynb", "planet.rst", "plot.rst", "propagation.rst", "trajopt.rst", "tut_basic.rst", "tut_trajopt.rst", "udpla.rst"], "titles": 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\ No newline at end of file
diff --git a/trajopt.html b/trajopt.html
index 3d2aeae..074c609 100644
--- a/trajopt.html
+++ b/trajopt.html
@@ -392,6 +392,11 @@ <h2> Contents </h2>
 <li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_point2point.pretty"><code class="docutils literal notranslate"><span class="pre">direct_point2point.pretty()</span></code></a></li>
 </ul>
 </li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_pl2pl"><code class="docutils literal notranslate"><span class="pre">direct_pl2pl</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_pl2pl.plot"><code class="docutils literal notranslate"><span class="pre">direct_pl2pl.plot()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_pl2pl.pretty"><code class="docutils literal notranslate"><span class="pre">direct_pl2pl.pretty()</span></code></a></li>
+</ul>
+</li>
 </ul>
 </li>
 </ul>
@@ -427,7 +432,7 @@ <h2>Direct<a class="headerlink" href="#direct" title="Permalink to this heading"
 <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">z</span> <span class="o">=</span> <span class="p">[</span><span class="n">mf</span><span class="p">,</span> <span class="n">throttles</span><span class="p">,</span> <span class="n">tof</span><span class="p">]</span>
 </pre></div>
 </div>
-<p>where throttles is a vector of throttles structures as [u0x, u0y,u0z, …]</p>
+<p>where throttles is a vector of throttles structures as [u0x, u0y,u0z, …]. By throttles we intend non dimensiona thrust levels in [0,1].</p>
 <p>Initializes the direct_point2point instance with given parameters.</p>
 <dl>
 <dt>Args:</dt><dd><p><em>rvs</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): Initial position and velocity vectors. Defaults to two vectors scaled by <code class="xref py py-class docutils literal notranslate"><span class="pre">AU</span></code> and Earth’s velocity.</p>
@@ -452,7 +457,7 @@ <h2>Direct<a class="headerlink" href="#direct" title="Permalink to this heading"
 <dd><p>Plots the trajectory leg  3D axes.</p>
 <dl>
 <dt>Args:</dt><dd><p><em>x</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): The decision vector containing final mass, thrust direction, and time of flight.</p>
-<p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>, optional): The 3D axis to plot on. Defaults to None.</p>
+<p><em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>, optional): The 3D axis to plot on. Defaults to None.</p>
 <p><em>units</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): The unit scale for the plot. Defaults to _pk.AU.</p>
 <p><em>show_midpoints</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>, optional): Whether to show midpoints on the trajectory. Defaults to False.</p>
 <p><em>show_gridpoints</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>, optional): Whether to show grid points on the trajectory. Defaults to False.</p>
@@ -461,7 +466,7 @@ <h2>Direct<a class="headerlink" href="#direct" title="Permalink to this heading"
 <p><em>arrow_length_ratio</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): Arrow length ratio for the throttle vectors. Defaults to 0.05.</p>
 <p><em>**kwargs</em>: Additional keyword arguments for the plot.</p>
 </dd>
-<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.0)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The 3D axis with the plotted trajectory.</p>
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The 3D axis with the plotted trajectory.</p>
 </dd>
 </dl>
 </dd></dl>
@@ -478,6 +483,73 @@ <h2>Direct<a class="headerlink" href="#direct" title="Permalink to this heading"
 
 </dd></dl>
 
+<dl class="py class">
+<dt class="sig sig-object py" id="pykep.trajopt.direct_pl2pl">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pykep.trajopt.</span></span><span class="sig-name descname"><span class="pre">direct_pl2pl</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="pre">pls=Planet</span> <span class="pre">name:</span> <span class="pre">earth</span> <span class="pre">-</span> <span class="pre">jpl_lp</span> <span class="pre">C++</span> <span class="pre">class</span> <span class="pre">name:</span> <span class="pre">kep3::udpla::jpl_lp</span>&#160; <span class="pre">mu</span> <span class="pre">central</span> <span class="pre">body</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">1.32712440018e+20</span> <span class="pre">mu</span> <span class="pre">body</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">398600441800000</span> <span class="pre">radius</span> <span class="pre">body</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">6378000</span> <span class="pre">safe</span> <span class="pre">body</span> <span class="pre">radius</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">7015800.000000001</span>&#160; <span class="pre">Extra</span> <span class="pre">info:</span>&#160; <span class="pre">Low-precision</span> <span class="pre">planet</span> <span class="pre">elements:</span>&#160; <span class="pre">Semi</span> <span class="pre">major</span> <span class="pre">axis</span> <span class="pre">(AU):</span> <span class="pre">1.00000261</span> <span class="pre">Eccentricity:</span> <span class="pre">0.01671123</span> <span class="pre">Inclination</span> <span class="pre">(deg.):</span> <span class="pre">-1.531e-05</span> <span class="pre">Big</span> <span class="pre">Omega</span> <span class="pre">(deg.):</span> <span class="pre">0</span> <span class="pre">Small</span> <span class="pre">omega</span> <span class="pre">(deg.):</span> <span class="pre">102.93768193</span> <span class="pre">True</span> <span class="pre">anomly</span> <span class="pre">(deg.):</span> <span class="pre">-2.557501705361543</span> <span class="pre">Mean</span> <span class="pre">anomly</span> <span class="pre">(deg.):</span> <span class="pre">-2.4731102699999923</span> <span class="pre">Elements</span> <span class="pre">reference</span> <span class="pre">epoch</span> <span class="pre">(MJD2000):</span> <span class="pre">0</span> <span class="pre">Elements</span> <span class="pre">reference</span> <span class="pre">epoch</span> <span class="pre">(date):</span> <span class="pre">2000-01-01T00:00:00.000000</span> <span class="pre">r</span> <span class="pre">at</span> <span class="pre">ref.</span> <span class="pre">=</span> <span class="pre">[-26504441615.311214,</span> <span class="pre">144693227461.25247,</span> <span class="pre">-38663.464067646026]</span> <span class="pre">v</span> <span class="pre">at</span> <span class="pre">ref.</span> <span class="pre">=</span> <span class="pre">[-29786.455213089437,</span> <span class="pre">-5478.770160337178,</span> <span class="pre">0.0014639816731285052]</span> <span class="pre">,</span> <span class="pre">plf=Planet</span> <span class="pre">name:</span> <span class="pre">mars</span> <span class="pre">-</span> <span class="pre">jpl_lp</span> <span class="pre">C++</span> <span class="pre">class</span> <span class="pre">name:</span> <span class="pre">kep3::udpla::jpl_lp</span>&#160; <span class="pre">mu</span> <span class="pre">central</span> <span class="pre">body</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">1.32712440018e+20</span> <span class="pre">mu</span> <span class="pre">body</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">42828000000000</span> <span class="pre">radius</span> <span class="pre">body</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">3397000</span> <span class="pre">safe</span> <span class="pre">body</span> <span class="pre">radius</span> <span class="pre">(-1</span> <span class="pre">if</span> <span class="pre">not</span> <span class="pre">defined):</span> <span class="pre">3736700.0000000005</span>&#160; <span class="pre">Extra</span> <span class="pre">info:</span>&#160; <span class="pre">Low-precision</span> <span class="pre">planet</span> <span class="pre">elements:</span>&#160; <span class="pre">Semi</span> <span class="pre">major</span> <span class="pre">axis</span> <span class="pre">(AU):</span> <span class="pre">1.52371034</span> <span class="pre">Eccentricity:</span> <span class="pre">0.0933941</span> <span class="pre">Inclination</span> <span class="pre">(deg.):</span> <span class="pre">1.84969142</span> <span class="pre">Big</span> <span class="pre">Omega</span> <span class="pre">(deg.):</span> <span class="pre">49.55953891</span> <span class="pre">Small</span> <span class="pre">omega</span> <span class="pre">(deg.):</span> <span class="pre">-73.5031685</span> <span class="pre">True</span> <span class="pre">anomly</span> <span class="pre">(deg.):</span> <span class="pre">23.37723882345258</span> <span class="pre">Mean</span> <span class="pre">anomly</span> <span class="pre">(deg.):</span> <span class="pre">19.390197540000006</span> <span class="pre">Elements</span> <span class="pre">reference</span> <span class="pre">epoch</span> <span class="pre">(MJD2000):</span> <span class="pre">0</span> <span class="pre">Elements</span> <span class="pre">reference</span> <span class="pre">epoch</span> <span class="pre">(date):</span> <span class="pre">2000-01-01T00:00:00.000000</span> <span class="pre">r</span> <span class="pre">at</span> <span class="pre">ref.</span> <span class="pre">=</span> <span class="pre">[208040933903.7969,</span> <span class="pre">-2003274684.4934082,</span> <span class="pre">-5155331001.447283]</span> <span class="pre">v</span> <span class="pre">at</span> <span class="pre">ref.</span> <span class="pre">=</span> <span class="pre">[1164.5634872088867,</span> <span class="pre">26297.05176199464,</span> <span class="pre">522.2478123931581]</span> <span class="pre">,</span> <span class="pre">ms=1500,</span> <span class="pre">mu=1.32712440018e+20,</span> <span class="pre">max_thrust=0.12,</span> <span class="pre">isp=3000,</span> <span class="pre">t0_bounds=[6700.0,</span> <span class="pre">6800.0],</span> <span class="pre">tof_bounds=[200.0,</span> <span class="pre">300.0],</span> <span class="pre">mf_bounds=[1300.0,</span> <span class="pre">1500.0],</span> <span class="pre">vinfs=3.0,</span> <span class="pre">vinff=0.0,</span> <span class="pre">nseg=10,</span> <span class="pre">cut=0.6,</span> <span class="pre">mass_scaling=1500,</span> <span class="pre">r_scaling=149597870700.0,</span> <span class="pre">v_scaling=29784.691831696804,</span> <span class="pre">with_gradient=True</span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.trajopt.direct_pl2pl" title="Permalink to this definition">#</a></dt>
+<dd><p>Represents the optimal low-thrust transfer between two <a class="reference internal" href="planet.html#pykep.planet" title="pykep.planet"><code class="xref py py-class docutils literal notranslate"><span class="pre">planet</span></code></a> using a direct method.</p>
+<p>This problem works internally using the <a class="reference internal" href="leg.html#pykep.leg.sims_flanagan" title="pykep.leg.sims_flanagan"><code class="xref py py-class docutils literal notranslate"><span class="pre">sims_flanagan</span></code></a> and manipulates its initial and final states, as well as its transfer time T, final mass mf
+and the controls as to link the two planets with a low-thrust trajectory.</p>
+<p>The particular transcription used is suitable only for few revolutions, after which convergence will start to be problematic.</p>
+<p>The decision vector is:</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">z</span> <span class="o">=</span> <span class="p">[</span><span class="n">t0</span><span class="p">,</span> <span class="n">mf</span><span class="p">,</span> <span class="n">Vsx</span><span class="p">,</span> <span class="n">Vsy</span><span class="p">,</span> <span class="n">Vsz</span><span class="p">,</span> <span class="n">Vfx</span><span class="p">,</span> <span class="n">Vfy</span><span class="p">,</span> <span class="n">Vfz</span><span class="p">,</span> <span class="n">throttles</span><span class="p">,</span> <span class="n">tof</span><span class="p">]</span> <span class="o">-</span> <span class="nb">all</span> <span class="ow">in</span> <span class="n">S</span><span class="o">.</span><span class="n">I</span><span class="o">.</span> <span class="n">units</span> <span class="k">except</span> <span class="n">t0</span> <span class="ow">and</span> <span class="n">tof</span> <span class="ow">in</span> <span class="n">days</span>
+</pre></div>
+</div>
+<p>where throttles is a vector of throttles structured as [u0x, u0y,u0z, …]. By throttles we intend non dimensiona thrust levels in [0,1].</p>
+<p>Initializes the direct_pl2pl instance with given parameters.</p>
+<dl>
+<dt>Args:</dt><dd><p><em>pls</em> (<a class="reference internal" href="planet.html#pykep.planet" title="pykep.planet"><code class="xref py py-class docutils literal notranslate"><span class="pre">planet</span></code></a>): Initial planet. Defaults to jpl_lp Earth.</p>
+<p><em>plf</em> (<a class="reference internal" href="planet.html#pykep.planet" title="pykep.planet"><code class="xref py py-class docutils literal notranslate"><span class="pre">planet</span></code></a>): Final planet. Defaults to jpl_lp Mars.</p>
+<p><em>ms</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Initial spacecraft mass in kg. Defaults to 1000 kg.</p>
+<p><em>mu</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Gravitational parameter, default is for the Sun (<code class="xref py py-class docutils literal notranslate"><span class="pre">MU_SUN</span></code>).</p>
+<p><em>max_thrust</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Maximum thrust in Newtons. Defaults to 0.12 N.</p>
+<p><em>isp</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Specific impulse in seconds. Defaults to 3000 s.</p>
+<p><em>t0_bounds</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): Bounds for departure epoch in MJD2000. Defaults to [6700.0, 6800.0].</p>
+<p><em>tof_bounds</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): Bounds for time of flight in days. Defaults to [200, 300] days.</p>
+<p><em>mf_bounds</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): Bounds for final mass in kg. Defaults to [1300.0, 1500.0] kg.</p>
+<p><em>vinfs</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Allowed magnitude for the departure’s relative velocity in km/s. Defaults to 3.</p>
+<p><em>vinff</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Allowed magnitude for the arrival’s relative velocity in km/s. Defaults to 0.</p>
+<p><em>nseg</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>): Number of segments for the trajectory. Defaults to 10.</p>
+<p><em>cut</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Cut parameter for the <a class="reference internal" href="leg.html#pykep.leg.sims_flanagan" title="pykep.leg.sims_flanagan"><code class="xref py py-class docutils literal notranslate"><span class="pre">sims_flanagan</span></code></a>. Defaults to 0.6.</p>
+<p><em>mass_scaling</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Scaling factor for mass (used to scale constraints). Defaults to 1500.</p>
+<p><em>r_scaling</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Scaling factor for distance, (used to scale constraints). Defaults AU (<code class="xref py py-class docutils literal notranslate"><span class="pre">AU</span></code>).</p>
+<p><em>v_scaling</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>): Scaling factor for velocity (used to scale constraints). Defaults the Earth’s velocity (<code class="xref py py-class docutils literal notranslate"><span class="pre">EARTH_VELOCITY</span></code>).</p>
+<p><em>with_gradient</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>): Indicates if gradient information should be used. Defaults True.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="pykep.trajopt.direct_pl2pl.plot">
+<span class="sig-name descname"><span class="pre">plot</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">units</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">149597870700.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_midpoints</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_gridpoints</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_throttles</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">arrow_length_ratio</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.05</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.trajopt.direct_pl2pl.plot" title="Permalink to this definition">#</a></dt>
+<dd><p>Plots the trajectory leg  3D axes.
+Args:</p>
+<blockquote>
+<div><p><em>x</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): The decision vector containing final mass, thrust direction, and time of flight.
+<em>ax</em> (<a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>, optional): The 3D axis to plot on. Defaults to None.
+<em>units</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): The unit scale for the plot. Defaults to _pk.AU.
+<em>show_midpoints</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>, optional): Whether to show midpoints on the trajectory. Defaults to False.
+<em>show_gridpoints</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>, optional): Whether to show grid points on the trajectory. Defaults to False.
+<em>show_throttles</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">bool</span></code></a>, optional): Whether to show throttle vectors. Defaults to False.
+<em>length</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): Length of the throttle vectors. Defaults to 0.1.
+<em>arrow_length_ratio</em> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, optional): Arrow length ratio for the throttle vectors. Defaults to 0.05.
+<em>**kwargs</em>: Additional keyword arguments for the plot.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>Returns:</dt><dd><p><a class="reference external" href="https://matplotlib.org/stable/api/toolkits/mplot3d/axes3d.html#mpl_toolkits.mplot3d.axes3d.Axes3D" title="(in Matplotlib v3.9.1)"><code class="xref py py-class docutils literal notranslate"><span class="pre">mpl_toolkits.mplot3d.axes3d.Axes3D</span></code></a>: The 3D axis with the plotted trajectory.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="pykep.trajopt.direct_pl2pl.pretty">
+<span class="sig-name descname"><span class="pre">pretty</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pykep.trajopt.direct_pl2pl.pretty" title="Permalink to this definition">#</a></dt>
+<dd><p>Prints a humar readable representation of the transfer.</p>
+<dl class="simple">
+<dt>Args:</dt><dd><p><em>x</em> (<a class="reference external" href="https://docs.python.org/3/library/stdtypes.html#list" title="(in Python v3.12)"><code class="xref py py-class docutils literal notranslate"><span class="pre">list</span></code></a>): The decision vector containing final mass, thrust direction, and time of flight.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
 </section>
 </section>
 
@@ -532,6 +604,11 @@ <h2>Direct<a class="headerlink" href="#direct" title="Permalink to this heading"
 <li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_point2point.pretty"><code class="docutils literal notranslate"><span class="pre">direct_point2point.pretty()</span></code></a></li>
 </ul>
 </li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_pl2pl"><code class="docutils literal notranslate"><span class="pre">direct_pl2pl</span></code></a><ul class="nav section-nav flex-column">
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_pl2pl.plot"><code class="docutils literal notranslate"><span class="pre">direct_pl2pl.plot()</span></code></a></li>
+<li class="toc-h4 nav-item toc-entry"><a class="reference internal nav-link" href="#pykep.trajopt.direct_pl2pl.pretty"><code class="docutils literal notranslate"><span class="pre">direct_pl2pl.pretty()</span></code></a></li>
+</ul>
+</li>
 </ul>
 </li>
 </ul>