AN INVESTIGATION OF THE STABILITY OF THE PERIODIC MOTION OF A RIGID-BODY WHEN THERE ARE COLLISIONS WITH A HORIZONTAL PLANE

The problem of the orbital stability of the translation-rotational mot ion of a rigid body in the shape of a circular disk above a fixed hori zontal plane in a uniform gravitational field is solved. It is assumed that the plane is absolutely smooth, the disk, is thin and homogeneou s and the collision of the disk with the plane is absolutely elastic. In the non-perturbed motion the plane of the disk is vertical, the dis k rotates with a constant angular velocity about the vertical or horiz ontal axis and its centre of gravity executes periodic oscillations al ong the fixed vertical as the result of the collisions.