File:Tennis racket effect.gif

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Tennis_racket_effect.gif ‎(480 × 480 pixels, file size: 4.67 MB, MIME type: image/gif, looped, 601 frames, 1 min 0 s)

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Captions

Captions

Visualization of the tennis racket theorem

Summary[edit]

Description
English: Tennis racket effect: a 3D body has 3 principal axis of rotation. If they are all distinct and you try to rotate it around the axis with intermediate inertia, any small perturbation will get amplified and the rotation direction will "flip".
Date
Source https://twitter.com/j_bertolotti/status/1271457003337125890
Author Jacopo Bertolotti
Permission
(Reusing this file)		 https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 12.0 code[edit]

body = RegionUnion[Cylinder[{{0, 0, -0.1}, {0, 0, 0.1}}, 1], Cylinder[{{0.9, 0, 0}, {2, 0, 0}}, 0.15]];
inertia = MomentOfInertia[body];
I1 = inertia[[1, 1]]; I2 = inertia[[2, 2]]; I3 = inertia[[3, 3]];
eeq1 = FullSimplify[I1 \[Omega]x'[t] + \[Omega]y[t] \[Omega]z[t] (I2 - I3)];
eeq2 = FullSimplify[I2 \[Omega]y'[t] + \[Omega]x[t] \[Omega]z[t] (I3 - I1)];
eeq3 = FullSimplify[I3 \[Omega]z'[t] + \[Omega]x[t] \[Omega]y[t] (I1 - I2)];
sol = NDSolve[{eeq1 == 0, eeq2 == 0, eeq3 == 0, \[Omega]x[0] == 0, \[Omega]y[0] == 1, \[Omega]z[0] == 0.001}, {\[Omega]x, \[Omega]y, \[Omega]z}, {t, 0, 60}];
cm = Chop@RegionCentroid@body;
dt = 0.1;
rot = IdentityMatrix[3];
rotation = Reap[For[t = 0, t <= 60, t = t + dt,
      axrot = Evaluate[{\[Omega]x[t], \[Omega]y[t], \[Omega]z[t]} /. sol][[1]];
      rot = RotationMatrix[dt*Norm[axrot], axrot].rot;
      Sow[Show[
        Graphics3D[{
          Dashed, Thick, Line[{-{0, 2, 0}, +{0, 2, 0}}]
          }, Boxed -> False, ViewVector -> {3 {1, 1, 1}, {0, 0, 0}}, ViewAngle -> 50*Degree],
        MapAt[GeometricTransformation[#, rot] &,
         Show[
          Graphics3D[{
            Yellow, 
            Translate[Cylinder[{{0, 0, -0.1}, {0, 0, 0.1}}, 1], -cm], 
            Translate[Cylinder[{{0.9, 0, 0}, {2, 0, 0}}, 0.15], -cm]}, 
           Boxed -> False, ViewVector -> {3 {1, 1, 1}, {0, 0, 0}}, ViewAngle -> 50*Degree]
          ], {1}]
        ]
       ];
      ];][[2, 1]];
ListAnimate[rotation]

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

File history

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Date/TimeThumbnailDimensionsUserComment
current08:52, 13 June 2020Thumbnail for version as of 08:52, 13 June 2020480 × 480 (4.67 MB)Berto (talk | contribs)Uploaded own work with UploadWizard

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