Ap. Markeyev, AN INVESTIGATION OF THE STABILITY OF THE PERIODIC MOTION OF A RIGID-BODY WHEN THERE ARE COLLISIONS WITH A HORIZONTAL PLANE, Journal of applied mathematics and mechanics, 58(3), 1994, pp. 445-456
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.