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 nf and the total time τc 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(nf)~exp[-θ₁nf] and P(τc)~exp[-θ₂τc]. The decay exponents θ₁ and θ₂ 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 θ₁ is provided for a particular case of the platform noise distribution.