|
This article is cited in 55 scientific papers (total in 55 papers)
Hamiltonization of Nonholonomic Systems in the Neighborhood of Invariant Manifolds
A.V. Bolsinova, A.V. Borisovb, I. S. Mamaevb a School of Mathematics, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom
b Institute of Computer Science, Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia
Abstract:
The problem of Hamiltonization of nonholonomic systems, both integrable and non-integrable, is considered. This question is important in the qualitative analysis of such systems and it enables one to determine possible dynamical effects. The first part of the paper is devoted to representing integrable systems in a conformally Hamiltonian form. In the second part, the existence of a conformally Hamiltonian representation in a neighborhood of a periodic solution is proved for an arbitrary (including integrable) system preserving an invariant measure. Throughout the paper, general constructions are illustrated by examples in nonholonomic mechanics.
Keywords:
conformally Hamiltonian system, nonholonomic system, invariant measure, periodic trajectory, invariant torus, integrable system.
Received: 17.12.2010 Accepted: 12.03.2011
Citation:
A.V. Bolsinov, A.V. Borisov, I. S. Mamaev, “Hamiltonization of Nonholonomic Systems in the Neighborhood of Invariant Manifolds”, Regul. Chaotic Dyn., 16:5 (2011), 443–464
Linking options:
https://www.mathnet.ru/eng/rcd446 https://www.mathnet.ru/eng/rcd/v16/i5/p443
|
Statistics & downloads: |
Abstract page: | 215 |
|