Nonholonomic Hamilton-Jacobi theory via Chaplygin Hamiltonization

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Ohsawa, Tomoki¹  Fernandez, Oscar E.²  Bloch, Anthony M.³  Zenkov, Dmitry V.⁴ 

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Univ Minnesota, Inst Math & Its Applicat, Minneapolis, MN 55455 USA

[3] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[4] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

关键词: Nonholonomic mechanics;    Hamilton-Jacobi theory;    Reduction;    Hamiltonization;   

DOI  :  10.1016/j.geomphys.2011.02.015

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier By. All rights reserved.

【 授权许可】

Free