-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathTennis_Racquet.nb
143 lines (119 loc) · 4.36 KB
/
Tennis_Racquet.nb
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 11.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 4309, 135]
NotebookOptionsPosition[ 3412, 101]
NotebookOutlinePosition[ 3755, 116]
CellTagsIndexPosition[ 3712, 113]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
StyleBox[
RowBox[{"Modeling", " ", "a", " ", "Tennis", " ", "Racquet"}],
"Title"]], "Input",
CellChangeTimes->{{3.7979463338962755`*^9, 3.797946336998512*^9}}],
Cell["Margaret Trautner | 18.303 | Spring 2020 (rip) | MIT", "Subsubsection",
CellChangeTimes->{{3.797946361519331*^9, 3.7979463856699743`*^9}}],
Cell[CellGroupData[{
Cell["Part I: Dynamic Beam Equation", "Section",
CellChangeTimes->{{3.7979464024839115`*^9, 3.7979464125354695`*^9}}],
Cell["\<\
As a first approximation to what happens to a tennis racket upon impact by a \
tennis ball, we will model the tennis racket as a beam with uniform density, \
uniform Young\[CloseCurlyQuote]s modulus, and uniform shape (and thus uniform \
second moment of area) along the beam. The equation describing the behavior \
of a beam under no tension is \
\>", "Text",
CellChangeTimes->{{3.7979464147860956`*^9, 3.7979464335728245`*^9}, {
3.797946483353221*^9, 3.7979465242543755`*^9}, {3.797946746387574*^9,
3.7979468094711103`*^9}}],
Cell["", "Text",
CellChangeTimes->{{3.797946973966921*^9, 3.797946992268512*^9}}],
Cell[CellGroupData[{
Cell["Derivation, solving the equation", "Subitem",
CellChangeTimes->{{3.7979593591627216`*^9, 3.797959369446398*^9}}],
Cell["Show the different modes figure", "Subitem",
CellChangeTimes->{{3.7979593591627216`*^9, 3.797959374205144*^9}}],
Cell[TextData[{
"Show the animation for the initial condition of y = ",
Cell[BoxData[
FormBox[
SuperscriptBox["x", "3"], TraditionalForm]],
FormatType->"TraditionalForm"]
}], "Subitem",
CellChangeTimes->{{3.7979593591627216`*^9, 3.7979593883282137`*^9}}]
}, Open ]],
Cell["\<\
Obviously, this doesn\[CloseCurlyQuote]t model a tennis racket super well. \
The tennis racket does is definitely not a beam of constant area, Young\
\[CloseCurlyQuote]s modulus, and density. We will come back to this later. \
\>", "Text",
CellChangeTimes->{{3.797959405679495*^9, 3.797959415431161*^9}, {
3.79795947598283*^9, 3.797959501745617*^9}}]
}, Open ]],
Cell[CellGroupData[{
Cell["Part II: 2D Wave Equation on an \[OpenCurlyDoubleQuote]Egg\
\[CloseCurlyDoubleQuote]", "Section",
CellChangeTimes->{{3.797959505353507*^9, 3.797959526295128*^9}}],
Cell["What about ", "Text",
CellChangeTimes->{{3.7979595298788676`*^9, 3.797959532165495*^9}}],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.797947049470484*^9, 3.797947050236467*^9}}],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.7979469699147425`*^9, 3.7979469708424306`*^9}}],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.797946960745309*^9, 3.797946968071325*^9}}],
Cell[BoxData[""], "Input",
CellChangeTimes->{{3.7979468863825607`*^9, 3.79794688699552*^9}}],
Cell["", "Text",
CellChangeTimes->{{3.797946828926823*^9, 3.7979468349754972`*^9}, {
3.7979468821744404`*^9, 3.797946883748549*^9}}]
}, Open ]]
},
WindowSize->{1280, 637},
WindowMargins->{{-8, Automatic}, {Automatic, -8}},
FrontEndVersion->"11.0 for Microsoft Windows (64-bit) (July 28, 2016)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 180, 4, 66, "Input"],
Cell[741, 26, 145, 1, 34, "Subsubsection"],
Cell[CellGroupData[{
Cell[911, 31, 118, 1, 49, "Section"],
Cell[1032, 34, 542, 9, 49, "Text"],
Cell[1577, 45, 82, 1, 30, "Text"],
Cell[CellGroupData[{
Cell[1684, 50, 119, 1, 25, "Subitem"],
Cell[1806, 53, 118, 1, 25, "Subitem"],
Cell[1927, 56, 264, 7, 27, "Subitem"]
}, Open ]],
Cell[2206, 66, 363, 6, 30, "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell[2606, 77, 169, 2, 63, "Section"],
Cell[2778, 81, 95, 1, 30, "Text"],
Cell[2876, 84, 92, 1, 30, "Input"],
Cell[2971, 87, 96, 1, 30, "Input"],
Cell[3070, 90, 92, 1, 30, "Input"],
Cell[3165, 93, 93, 1, 30, "Input"],
Cell[3261, 96, 135, 2, 30, "Text"]
}, Open ]]
}
]
*)