The stability of periodic trajectories of a billiard ball in three dimensions
The stability of periodic trajectories of a material point moving between two convex walls with elastic reflections is investigated. The problem is closely bound related to wave propagation theory in the shortwave approximation. The simplest periodic trajectory is a section of a straight line orthogonal to the wall at its endpoints. The problem of the stability of a two-part trajectory will be solved here in three dimensions.
scientific article; zbMATH DE number 500812
scientific article