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arXiv · 1102.4361

Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization

Tomoki Ohsawa·Oscar E. Fernandez·Anthony M. Bloch·Dmitry V. Zenkov
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Abstract

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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Tomoki Ohsawa, Oscar E. Fernandez, Anthony M. Bloch, Dmitry V. Zenkov. 2011-02-21. Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization. https://doi.org/10.1016/j.geomphys.2011.02.015

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