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This article is cited in 13 scientific papers (total in 13 papers)
One Invariant Measure and Different Poisson Brackets for Two Non-Holonomic Systems
Andrey V. Tsiganov St. Petersburg State University, ul. Ulyanovskaya 1, St. Petersburg, 198504 Russia
Abstract:
We discuss the non-holonomic Chaplygin and the Borisov–Mamaev–Fedorov systems, for which symplectic forms are different deformations of the square root from the corresponding invariant volume form. In both cases second Poisson bivectors are determined by $L$-tensors with non-zero torsion on configuration space, in contrast with the well-known Eisenhart–Benenti and Turiel constructions.
Keywords:
non-holonomic mechanics, Chaplygin’s rolling ball, Poisson brackets.
Received: 28.10.2011 Accepted: 29.12.2011
Citation:
Andrey V. Tsiganov, “One Invariant Measure and Different Poisson Brackets for Two Non-Holonomic Systems”, Regul. Chaotic Dyn., 17:1 (2012), 72–96
Linking options:
https://www.mathnet.ru/eng/rcd384 https://www.mathnet.ru/eng/rcd/v17/i1/p72
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Abstract page: | 90 |
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