J. Phys. I France
Volume 4, Numéro 7, July 1994
Page(s) 1003 - 1011
DOI: 10.1051/jp1:1994180
J. Phys. I France 4 (1994) 1003-1011

Dynamics of a ball on a vibrating plate

P. Devillard

Centre de Physique Théorique de Marseille, CNRS Luminy, Case 907, CPT, 13288 Marseille Cedex 9, France

(Received 3 February 1994, received in final form 18 March 1994, accepted 23 March 1994)

We study both analytically and numerically the problem of a partially inelastic ball on a platform vibrating with frequency $\omega$. Two parameters control the dynamics, the restitution coefficient $\eta$, and the reduced acceleration $\Gamma = \gamma/g$, where $\gamma$ is the maximum acceleration of the motion of the plate and g the acceleration of gravity. When $\eta$ exceeds some value, simple stable fixed points no longer exist, but it is shown that generic trajectories are periodic with period TB which behaves as $T_B \sim (1 - \eta)^{-5}$ for $\eta$ close to 1.

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