On the Motion of a Ball between Rotating Planes with Viscous Friction

Abstract

The problem of the motion of a ball between two uniformly rotating horizontal planes with linear viscous friction is considered. Steady motions of the ball are found and the parameters of the system under which these motions are stable or unstable are indicated. It is shown that the equations of motion of a low-inertia ball have the form of Tikhonov’s equations with a small parameter as a coefficient at some derivatives. The dynamics of this ball on an arbitrary finite time interval in the limit as the central moment of inertia of the ball tends to zero is studied.