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Mat. Zametki, 2014, Volume 95, Issue 3, Pages 340–349 (Mi mz10422)  

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

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.

DOI: https://doi.org/10.4213/mzm10422

Full text: PDF file (422 kB)
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English version:
Mathematical Notes, 2014, 95:3, 308–315

Bibliographic databases:

Document Type: Article
UDC: 531.38+517.925
Received: 28.05.2013

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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  • https://doi.org/10.4213/mzm10422
  • http://mi.mathnet.ru/eng/mz/v95/i3/p340

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bizyaev I.A., “Nonintegrability and Obstructions To the Hamiltonianization of a Nonholonomic Chaplygin TOP”, Dokl. Math., 90:2 (2014), 631–634  crossref  mathscinet  zmath  isi  scopus
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