Inelastic collapse of a ball bouncing on a randomly vibrating platform

A theoretical study is undertaken of the dynamics of a ball which is bouncing inelastically on a randomly vibrating platform. Of interest are the distributions of the number of flights n(f) and the total time tau(c) until the ball has effectively collapsed, i.e., coalesced with the platform. In the strictly elastic case both distributions have power law tails characterized by exponents that are universal, i.e., independent of the detail of the platform noise distribution. However, in the inelastic case both distributions have exponential tails: P(n(f))similar to exp[-theta(1)n(f)] and P(tau(c))similar to exp[-theta(2)tau(c)]. The decay exponents theta(1) and theta(2) depend continuously on the coefficient of restitution and are nonuniversal; however, as one approaches the elastic limit, they vanish in a manner which turns out to be universal. An explicit expression for theta(1) is provided for a particular case of the platform noise distribution.