The Motion of a Rolling Polygon

Abstract

Galileo was the first to analyze the motion of spheres rolling down an inclined surface. Since then, Coulomb’s law of dry friction has covered the case of sliding particles. However, a particle that is not round can still roll, although in a way that is essentially different from the motion studied by Galileo. Instead of keeping contact with the surface, such particles will start bouncing after reaching a certain angular velocity. This motion is a combination of flying and colliding. It is shown that the acceleration of a bouncing particle is always bounded by the accelerations for perfect rolling and sliding. In order to describe the motion of a not perfectly round particle, the polygon is used as a model. The aim of the model is to predict the trajectories of particles that cannot be covered by the models for perfect rolling and sliding.