Dzhanibekov

Dzhanibekov Effect aka Tennis Racket Theorem


The Dzhanibekov Effect or Tennis Racket Theorem describes the curious effect observed for the rotation of an object under zero gravitation as seen in the NASA video clip on the left: For a body with three distinct moments of inertia, rotation around the principal axis with the intermediate moment is unstable and leads to the seen rapid orientation flips. The middle and right movie show my numerical solution of Euler's equations for the motion of the massless disk seen on the right, to which four balls are attached, two heavy and two light ones, with a mass ratio of 10:1 (Mathematica code). The middle animation shows the temporal evolution of the orientation of the three principal axes. There exists even an analytic solution for this problem involving Jacobi elliptic functions. The fabulous Terry Tao has presented, in my view, one of the best explanations of this effect, and the above animation is directly related to his explanation.
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