Abstract
The classical phenomenon of a sphere transitioning from sliding to rolling during its motion on a horizontal plane is investigated from a novel system theoretic perspective. Specifically, the transition is studied as a problem in stabilization, an approach not reported in the literature. The main contribution of this paper is in proving that pure rolling is an asymptotically stable equilibrium within the state-space of a sliding sphere. It is shown that the stabilization of this equilibrium from arbitrary initial conditions occurs through the natural interplay between the friction force and moment that result from sliding. Simulation results confirm the theoretical development. The stability analysis is extended to motion on an inclined plane.
