It is shown that the free motion of any three-dimensional rigid body colliding elastically between two parallel, flat 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 field and a non-Euclidean configuration 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.

• Received 27 November 1995

DOI:https://doi.org/10.1103/PhysRevE.53.5670