ИСТИНА

The problem of the motion of a low-inertia ball between two horizontal uniformly rotating planes with linear viscous friction is considered. The center of mass of the ball coincides with its geometric center, the central inertia tensor of the ball is spherical. Two cases of low inertia of the ball are investigated: in the first case the mass of the ball is constant and concentrated near its center, in the second case the mass of the ball is small. The dynamics of the ball on an arbitrary finite time interval in the limit as the central moment of inertia of the ball tends to zero is studied. In both cases the equations of motion of the ball have the form of the Tikhonov’s type equations with a small parameter in the left-hand side. In the first case it is shown that in the limit the center of mass of the ball moves as a material point located between horizontal rotating planes with linear viscous friction. In the second case the dynamics of the ball in the limit coincides with the dynamics of a homogeneous ball moving between two absolutely rough rotating planes.