NONHOLONOMIC CONTROL-SYSTEMS ON RIEMANNIAN-MANIFOLDS

This paper gives a general formulation of the theory of nonholonomic control systems on a Riemannian manifold modeled by second-order differential equations and using the unique Riemannian connection defined by the metric. The main concern is to introduce a reduction scheme, replacing some of the second-order equations by first-order equations. The authors show how constants of motion together with the nonholonomic constraints may be combined to yield such a reduction. The theory is applied to a particular class of nonholonomic control systems that may be thought of as modeling a generalized rolling ball. This class reduces to the classical example of a ball rolling without slipping on a horizontal plane.