The Dynamics of a Forced Sphere-Plate Mechanical System

Abstract

We study the dynamics and explore thecontrollability of a family of sphere-plate mechanical systems. Theseare nonholonomic systems with a five-dimensional configuration spaceand three independent velocities. They consist of a sphere rollingin contact with two horizontal plates. Kinematic models ofsphere-plate systems have played an important role in the controlsystems literature addressing the kinematics of rolling bodies, aswell as in discussions of nonholonomic systems. However, kinematicanalysis falls short of allowing one to understand the dynamicbehavior of such systems. In this work we formulate and study adynamic model for a class of sphere-plate systems in order to answerthe question: "Is it possible to impart a net angular momentum to asphere which rolls without slipping between two plates, given thatthe position of the top plate is subject to exogenousforces?"The research and scientific content in this material will appearin IEEE Transactions on Automatic Control.