Feature request: Cotangent space

[GiulioRomualdi]

Hi @artivis, we are currently your library in our lab. We see that for each Liegroup, manif exposes the associated tangent space but not the cotangent one.
I was wondering if there is a reason why it is not implemented and if there is any possible plan to add it.

cc @RiccardoGrieco

[artivis]

Hi @GiulioRomualdi,
There is no plan to add this at the moment but if you'd like to discuss one we can do so. I guess the first step would be to put together some math doc to clarify the topic and set some solid foundations.
cc @joansola

[joansola]

Agree. I never digged into the cotangent space, and I am just reading about it rapidly. I have a few questions: Given a group, is the cotangent space unique? As it is the tangent space? Or are there many possible cotangent spaces? If it is unique, I guess we could add all its functionality, as we did with the Tangent. What would this functionality consist of? Any idea of what functions / operators / objects are needed? And a side question: what do you use the cotangent space for? Joan

…

On 17 Feb 2023, at 13:03, Jeremie Deray ***@***.***> wrote: Hi @GiulioRomualdi <https://github.com/GiulioRomualdi>, There is no plan to add this at the moment but if you'd like to discuss one we can do so. I guess the first step would be to put together some math doc to clarify the topic and set some solid foundations. cc @joansola <https://github.com/joansola> — Reply to this email directly, view it on GitHub <#263 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAS2LPLWPX5CEGITDGOLHR3WX5SKFANCNFSM6AAAAAAU43BJ2M>. You are receiving this because you were mentioned.

[rebcabin]

The cotangent space seems essential for control applications, as directional derivatives (cotangent covectors) applied to the potential energy effect d'Alembert's Principle. Please see the right-most terms in Equations 16b and 16c of this paper: https://arxiv.org/abs/1609.02898.