The theory of mechanical systems with nonholonomic constraints has a long history in classical mechanics; see e.g. the books by Neimark & Fufaev [14], Edelen [6], Rosenberg [16], Arnold [l] and the references quoted in there. In this literature, nonholonomic mechanical systems are described within the variational framework by Euler-Lagrange equations with extra terms corresponding to the constr...

This paper continues the work of Koon and Marsden [1997b] that began the comparison of the Hamiltonian and Lagrangian formulations of nonholonomic systems. Because of the necessary replacement of conservation laws with the momentum equation, it is natural to let the value of momentum be a variable and for this reason it is natural to take a Poisson viewpoint. Some of this theory has been starte...

Abstract In this paper a dexterity measure is proposed for driftless nonholonomic systems. Admissible motions at a given state of a nonholonomic system are described by the controllability (Lie) algebra of the system. The algebra is completely described by Lie monomials (vector fields) produced by the Lie bracketing of vector fields associated with the system. At a given state, the nonholonomic...