Friction-Dependent Chaotic Dynamics. A Bouncing Disk on a Saw Tooth
J. Duran · Europhysics Letters (EPL) · 1992
A two-dimensional model of a hard disk bouncing in a ballistic motion on a 2D horizontal saw tooth structure is investigated using classical-mechanics equations for inelastic shocks including a solid-friction parameter. In the various relevant cases, the numerical iteration of the relevant nonlinear equations over a number of successive impacts display the characteristics of transitions to chaos: large sensitivity to initial conditions and a series of bifurcations depending on the dissipation coefficient. The intermediate case where the friction parameter is neither zero nor large enough to lead to a sliding velocity cancelling out before the end of the shock, is shown to induce, at least in the chaotic regime, a unidirectional motion of the disk which goes on, all along the process. In both other cases which concern the frictionless or the strong-friction situations, the disk is seen to undergo an expected back and forth motion which fulfils the 2D symmetry of the system. Tentatively, we suggest that solid friction, at least in the intermediate regime, might play a significant role in the breaking of symmetry of the overall motion as observed in several recent shaken multiparticle experiments.