Rotation in a gravitational billiard

Abstract

Gravitational billiards composed of a viscoelastic frictional disk bouncing on a vibrating wedge have been studied previously, but only from the point of view of their translational behavior. In this work, the average rotational velocity of the disk is studied under various circumstances. First, an experimental realization is briefly presented, which shows sustained rotation when the wedge is tilted. Next, this phenomenon is scrutinized in close detail using a precise numerical implementation of frictional forces. We show that the bouncing disk acquires a spontaneous rotational velocity whenever the wedge angle is not bisected by the direction of gravity. Our molecular dynamics (MD) results are well reproduced by event-driven (ED) simulations. When the wedge aperture angle [Formula: see text], the average tangential velocity [Formula: see text] of the disk scales with the typical wedge vibration velocity [Formula: see text], and is in general a nonmonotonic function of the overall tilt angle [Formula: see text] of the wedge. The present work focuses on wedges with [Formula: see text], which are relevant for the problem of spontaneous rotation in vibrated disk packings. This study makes part of the PhD Thesis of G. G. Peraza-Mues.