Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
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.
Keywords
Cite
@article{arxiv.1102.4361,
title = {Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization},
author = {Tomoki Ohsawa and Oscar E. Fernandez and Anthony M. Bloch and Dmitry V. Zenkov},
journal= {arXiv preprint arXiv:1102.4361},
year = {2011}
}
Comments
Accepted for publication in Journal of Geometry and Physics