Absence of inelastic collapse in a realistic three ball model

Inelastic collapse, the process in which a number of partially inelastic balls dissipate their energy through an infinite number of collisions in a finite amount of time, is studied for three balls on an infinite line and on a ring (i.e., a line segment with periodic boundary conditions). Inelastic collapse has been shown to exist for systems in which collisions occur with a coefficient of restitution $r$ independent of the relative velocities of the colliding particles. In the present study, a more realistic model is assumed for $r:$ $r=1\mathrm{}$ for relative velocity equal to zero, and $r$ decreases monotonically for increasing relative velocity. With this model, inelastic collapse does not occur for three balls on a line or a ring.