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Matematicheskie Zametki, 2014, Volume 95, Issue 3, Pages 340–349
DOI: https://doi.org/10.4213/mzm10422 (Mi mzm10422) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics

A. V. Borisovab, I. S. Mamaevb, A. V. Tsiganovc

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Udmurt State University, Izhevsk
c Saint Petersburg State University
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DOI: https://doi.org/10.4213/mzm10422
Abstract: Nonholonomic systems describing the rolling of a rigid body on a plane and their relationship with various Poisson structures are considered. The notion of generalized conformally Hamiltonian representation of dynamical systems is introduced. In contrast to linear Poisson structures defined by Lie algebras and used in rigid-body dynamics, the Poisson structures of nonholonomic systems turn out to be nonlinear.
Keywords: Poisson bracket, nonholonomic system, Poisson structure, dynamical system, conformally Hamiltonian representation, Casimir function, Routh sphere, rolling of a Chaplygin ball.
Received: 28.05.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 3, Pages 308–315
DOI: https://doi.org/10.1134/S0001434614030031
Bibliographic databases:
Document Type: Article
UDC: 531.38+517.925
Language: Russian
Citation: A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics”, Mat. Zametki, 95:3 (2014), 340–349; Math. Notes, 95:3 (2014), 308–315
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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