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.