File:Belt trick 2.gif
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Summary
| Description | Illustration of the belt trick, showing a homotopy between two one-parameter subgroups of the rotation group, one through an angle of 2π and one through an angle of −2π. |
| Date | |
| Source | Created in Mathematica 9.0 (source code below) |
| Author | Slawekb |
- Source
F1[s_, t_] = {{E^(2 \[Pi] I t), Tan[][Pi] s/2]}, {-Tan[][Pi] s/2],
E^(-2 \[Pi] I t)}}.{{E^(-\[Pi] I t), 0}, {0, E^(\[Pi] I t)}}
F2[s_, t_] = (F1[s, t]/Sqrt[][][s, t]])
F[s_, t_] = FullSimplify[][][s, 0].F2[s, t]
Clear[i, j, k]
i = {{I, 0}, {0, -I}};
j = {{0, -1}, {1, 0}};
k = i.j;
Components[A_] := (1/2) {Tr[][i],
Tr[][j], Tr[][k]}
R[s_][t_] =
Transpose[][][][][s, t].i.ConjugateTranspose[][s, t]]]],
FullSimplify[][][][s, t].j.ConjugateTranspose[][s, t]]]],
FullSimplify[][][][s, t].k.ConjugateTranspose[][s, t]]]]}];
PlotRotation[R_] :=
ParametricPlot3D[][t][[1]] t + R[t][[2]] s, {t, 0, 1}, {s, 0, 1/7.5},
Boxed -> False, Axes -> False, PlotPoints -> 20,
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}}, Mesh -> {0, 3},
ImageSize -> 768]
b = Join[][][][s], {s, 0.01, 0.99, 0.02}],
Table[][][s], {s, 0.99, 0.01, -0.02}]];
Export["b.gif", b]
Licensing
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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Original upload log
The original description page was here. All following user names refer to en.wikipedia.
| Date/Time | Dimensions | User | Comment |
|---|---|---|---|
| 14:19, September 7, 2014 | 533 × 391 (366 KB)) | Slawekb |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:56, 15 June 2016 | | 533 × 391 (366 KB) | Bruno Max Melo | ==Summary== {{Information |Description = Illustration of the belt trick, showing a homotopy between two one-parameter subgroups of the rotation group, one through an angle of 2π and one through an angle of −2π. |Source = Created in Mathemat... |
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