Rigid-body motion, interacting billiards, and billiards on curved manifolds.

It is shown that the free motion of any three-dimensional rigid body colliding elastically between two parallel, at walls is equivalent to a three-dimensional billiard system. Depending upon the inertial parameters of the problem, the billiard system may possess a potential energy eld and a non-Euclidean connguration space. The corresponding curvilinear motion of the billiard ball does not necessarily lead to a decrease of the stable periodic orbits found in the analogous rectilinear system.