Mode bifurcation of a bouncing dumbbell with chirality

Abstract

We studied the behavior of a dumbbell bouncing upon a sinusoidally vibrating plate. By introducing chiral asymmetry to the geometry of the dumbbell, we observed a cascade of bifurcations with an increase in the vibration amplitude: spinning, orbital, and rolling. In contrast, for an achiral dumbbell, bifurcation is generated by a change from random motion to vectorial inchworm motion. A simple model particle was considered in a numerical simulation that reproduced the essential aspects of the experimental observation. The mode bifurcation from directional motion to random motion is interpreted analytically by a simple mechanical discussion.