Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization

Details Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization

2011-02-21

arxiv.org/abs/1102.4361v2

Journal of Geometry and Physics, 61 (2011), pp. 1263-1291

Physics

Mathematical Physics

Accepted for publication in Journal of Geometry and Physics

Scientific paper

10.1016/j.geomphys.2011.02.015

We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a geometric account of the Hamiltonization, identify necessary and sufficient conditions for Hamiltonization, and apply the conventional Hamilton-Jacobi theory to the Hamiltonized systems. We show, under a certain sufficient condition for Hamiltonization, that the solutions to the Hamilton-Jacobi equation associated with the Hamiltonized system also solve the nonholonomic Hamilton-Jacobi equation associated with the original Chaplygin system. The results are illustrated through several examples.

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