File:Animation of Heisenberg geodesic.gif
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Animation_of_Heisenberg_geodesic.gif (315 × 432 pixels, file size: 285 KB, MIME type: image/gif, looped, 62 frames)
Summary
| Description |
English: This is an animation of a typical geodesic in the Heisenberg group, parameterized by arc-length. |
| Date | |
| Source | Created in mathematica, using equation 2.23 of Capogna et al "Introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem" |
| Author | Slawekb |
- Other information
Mathematica source:
R[f_] := {Re[f1], Im[f1], f2}
\[Gamma][c_, \[Phi]_][s_] =
R[{E^(I \[Phi]) (1 - E^(-I c s))/c, (c s - Sin[c s])/(2 c^2)}] //
ComplexExpand
u[S_] := ParametricPlot3D[{\[Gamma][1, 0][s]1 t, \[Gamma][1, 0][
s][2] t, 0}, {s, 0, S}, {t, 0, 1}, Mesh -> False]
v[S_] := ParametricPlot3D[\[Gamma][1, 0][s], {s, 0, S}]
PlotTab =
Table[Show[u[S], v[S],
PlotRange -> {{0, 2}, {-1, 1}, {0, \[Pi]}}], {S, 0.1, 2 \[Pi],
0.1}];
Export["heis.gif", PlotTab]
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
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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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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:12, 3 May 2016 | | 315 × 432 (285 KB) | wikimediacommons>Slawekb | Uploading a self-made file using File Upload Wizard |
File usage
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