The tennis racket theorem, demonstrated in a Soviet space station. (Via Math Overflow.)

(The tennis racket theorem asserts that when rotating a rigid body with three distinct moments of inertia, the rotation around the axes with the largest or smallest moments of inertia is stable, but the rotation around the axis with the intermediate moment of inertia is unstable. Indeed, in the latter case the object will (when one looks just at the angular velocities) typically traverse periodically through the space of all states with the given angular momentum and energy, which is a closed curve known as a herpolhode that will pass close to both antipodes of the unstable equilibrium in an alternating fashion.)
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