J. Phys. I France 4 (1994) 1003-1011
Dynamics of a ball on a vibrating plateP. 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 . Two parameters control the dynamics, the restitution coefficient , and the reduced acceleration , where is the maximum acceleration of the motion of the plate and g the acceleration of gravity. When 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 for close to 1.
© Les Editions de Physique 1994