Periodic orbits of a one-dimensional inelastic particle system

The dynamical behavior of a one-dimensional inelastic particle system with two particles of different masses traveling between two walls is investigated. Energy is added at only one of the walls, which is oscillating, while the other wall is stationary. We show that if the particle nearer to the stationary wall is slightly lighter than the other particle and collisions between particles tend to the elastic limit, there are an infinite number of stable orbits. We also show that the widely studied situation of equal masses is an extremely special case, in which all the orbits are degenerate and collapse to a single trivial orbit in which one of the particles is trapped against the stationary wall. To cite this article: J.J. Wylie, Q. Zhang, C. R. Acad. Sci. Paris, Ser. I 339 (2004).