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Inelastic Collapse of Three Particles

Tong Zhou·Leo Kadanoff
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Abstract

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, 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 $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.

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Tong Zhou, Leo Kadanoff. 1996-04-10. Inelastic Collapse of Three Particles. https://doi.org/10.1103/physreve.54.623

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