On the motion of a solid with an ideal non-retaining constraint

Abstract

The extension of method /1/ of canonical formalism to systems with ideal one-way constraints are applied to the analysis of the motion of a solid when it collides with a stationary horizontal absolutely smooth plane. The surface of the body is assumed to be close to a sphere. The Kolmogorov theorem on the conservation of motion when there is a small change in the Hamiltonian functions /2, 3/ is used for a qualitative investigation of the motion of the body. The existence of periodic motions of an homogeneous ellipsoid of revolution is proved by Poincaré's method /4/ and their stability is investigated.