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.
- Publication:
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Journal of Geometry and Physics
- Pub Date:
- August 2011
- DOI:
- 10.1016/j.geomphys.2011.02.015
- arXiv:
- arXiv:1102.4361
- Bibcode:
- 2011JGP....61.1263O
- Keywords:
-
- Mathematical Physics;
- Mathematics - Dynamical Systems;
- Mathematics - Symplectic Geometry;
- 70F25;
- 70H06;
- 70H20
- E-Print:
- Accepted for publication in Journal of Geometry and Physics