Inelastic collapse of three particles.

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of {open_quote}{open_quote}inelastic collapse{close_quote}{close_quote}{emdash}an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, 0{le}{ital r}{lt}7{minus}4{radical}3{approx_equal}0.072, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller {ital r} range, 0{le}{ital r}{lt}9{minus}4{radical}5{approx_equal}0.056. {copyright} {ital 1996 The American Physical Society.}