Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations

Details Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations

2008-12-02

arxiv.org/abs/0812.0437v1

Rep. Math. Phys. 63 (2009) 225-249.

Physics

Mathematical Physics

23 pages, accepted for publication in Rep. Math. Phys

Scientific paper

We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations to an appropriate submanifold of phase space. We focus first on the Lagrangian picture of the method and deduce the corresponding Hamiltonian from the Legendre transformation. We illustrate the method with several examples and we discuss its relationship to the Pontryagin maximum principle.

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