Abstract
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 constraint submanifold, and then trying to start a Hamiltonization procedure from there. We prove a theorem concerning the regularity which is required to obtain a unique second-order dynamics on the constraint submanifold, and we show that the same condition allows the transition to a Hamiltonian picture. Throughout the analysis, different degrees of generality are discussed.
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