Simplest piston problem. II. Inelastic collisions.

We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy "piston," with elastic collisions between particles but inelastic collisions between the light particles and the interval ends. A symmetry breaking occurs in which the piston migrates near one end of the interval and performs small-amplitude periodic oscillations on a logarithmic time scale. The properties of this dissipative limit cycle can be understood simply in terms of a effective restitution coefficient picture. Many dynamical features of the three-particle system closely resemble those of the many-body inelastic piston problem.