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# Geodesics in Rotating Frame

Matthen May 14th, 2013 230 Never
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1. n = 6;
2. \[Omega] = 1/2;
3. p1s = Table[{-Sqrt[1 - y^2], y}, {y, -1, 1, 2/n}][[2 ;; -2]];
4. p1s2 = Table[{x, -Sqrt[1 - x^2]}, {x, -1, 1, 2/n}][[2 ;; -2]];
5. Manipulate[
6.  Show[
7.   Graphics[{
8.     Circle[{0, 0}, 1],
9.     Table[
10.      Line[{{Sin[\[Theta] + \[Omega] t],
11.         Cos[\[Theta] + \[Omega] t]}, {Sin[\[Theta] + \[Omega] t + Pi],
12.          Cos[\[Theta] + \[Omega] t + Pi]}}],
13.      {\[Theta], 0, Pi, Pi/5}],
14.     Table[
15.      Block[{
16.        pt =
17.         p1 Max[0, (1 - (t/(2 Pi))/(-p1[[1]]))] + {-p1[[1]],
18.            p1[[2]]} Min[1, (t/(2 Pi))/(-p1[[1]])]
19.        },
20.       {Disk[pt, 0.05],
21.        Opacity[0.5], Darker[Red], Line[{p1, pt}]
22.        }]
23.      , {p1, p1s}],
24.     Table[
25.      Block[{
26.        pt =
27.         p1 Max[0, (1 - (t/(2 Pi))/(-p1[[2]]))] + {p1[[
28.             1]], -p1[[2]]} Min[1, (t/(2 Pi))/(-p1[[2]])]
29.        },
30.       {Disk[pt, 0.05],
31.        Opacity[0.5], Darker[Red], Line[{p1, pt}]
32.        }]
33.      , {p1, p1s2}]
34.     }, PlotRange -> 1.1],
35.   Table[
36.    ParametricPlot[
37.     RotationMatrix[\[Omega] (\[Tau] - t)].(
38.       p1 Max[0, (1 - (\[Tau]/(2 Pi))/(-p1[[1]]))] + {-p1[[1]],
39.          p1[[2]]} Min[1, (\[Tau]/(2 Pi))/(-p1[[1]])]
40.       )
41.     , {\[Tau], -0.001, t}, PlotStyle -> Thick]
42.    , {p1, p1s}
43.    ],
44.   Table[
45.    ParametricPlot[
46.     RotationMatrix[\[Omega] (\[Tau] - t)].(
47.       p1 Max[
48.          0, (1 - (\[Tau]/(2 Pi))/(-p1[[2]]))] + {p1[[
49.           1]], -p1[[2]]} Min[1, (\[Tau]/(2 Pi))/(-p1[[2]])]
50.       )
51.     , {\[Tau], -0.001, t}, PlotStyle -> Thick]
52.    , {p1, p1s2}
53.    ]
54.   ],
55.  {t, 0, 2 Pi}
56.  ]
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