Nonholonomic Hamilton-Jacobi theory via Chaplygin Hamiltonization

作者：Ohsawa Tomoki^*; Fernandez Oscar E; Bloch Anthony M; Zenkov Dmitry V

来源：Journal of Geometry and Physics, 2011, 61(8): 1263-1291.

DOI：10.1016/j.geomphys.2011.02.015

• Nonholonomic mechanics
• Hamilton-Jacobi theory
• Reduction
• Hamiltonization

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.

• 出版日期2011-8