Regularity aspects and Hamiltonization of non-holonomic systems

We discuss various aspects of the transition from Lagrangian to Hamiltonian equations for systems with general (nonlinear) non-holonomic constraints. The emphasis is first on constructing the reduced dynamics on the constrain t submanifold, and then trying to start a Hamiltonization procedure from th ere. We prove a theorem concerning the regularity which is required to obta in a unique second-order dynamics on the constraint submanifold, and we sho w that the same condition allows the transition to a Hamiltonian picture. T hroughout the analysis, different degrees of generality are discussed.