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→Geometric analysis: tennis racket effect |
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* They intersect at two cycles around the points <math>(\pm L / I_1, 0, 0)</math>. Since each cycle contains no point at which <math>\dot\omega=0</math>, the motion of <math>\omega(t)</math> must be a periodic motion around each cycle.
* The energy ellipsoid last intersects the momentum ellipsoid when <math>2E = L^2/I_1</math>, at the points <math>(\pm L / I_1, 0, 0)</math>. This is when the body rotates around its axis with the smallest moment of inertia.
The tennis racket effect occurs when <math>\omega(0)</math> is very close to a saddle point. The body would linger near the saddle point, then rapidly move to the other saddle point, repeating periodically.
== See also ==
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