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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 5, Pages 439–450
DOI: https://doi.org/10.1134/S1560354712050061 (Mi rcd414) 		 
This article is cited in 16 scientific papers (total in 16 papers)

On the Poisson Structures for the Nonholonomic Chaplygin and Veselova Problems

Andrey V. Tsiganov

St.Petersburg State University, ul. Ulyanovskaya 1, St. Petersburg, 198504 Russia
Citations (16)
DOI: https://doi.org/10.1134/S1560354712050061
Abstract: We discuss a Poisson structure, linear in momenta, for the generalized nonholonomic Chaplygin sphere problem and the $LR$ Veselova system. Reduction of these structures to the canonical form allows one to prove that the Veselova system is equivalent to the Chaplygin ball after transformations of coordinates and parameters.
Keywords: nonholonomic mechanics, Poisson brackets.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
The work was done at the Udmurt State University and was supported by the Grant Program of the Government of the Russian Federation for Support for the Scientific Research Project implemented under the supervision of leading scientists at Russian institutions of higher education (11.G34.31.0039).
Received: 20.05.2012
Accepted: 30.07.2012
Bibliographic databases:
Document Type: Article
MSC: 37J60
Language: English
Citation: Andrey V. Tsiganov, “On the Poisson Structures for the Nonholonomic Chaplygin and Veselova Problems”, Regul. Chaotic Dyn., 17:5 (2012), 439–450
Citation in format AMSBIB
\Bibitem{Tsi12}
\by Andrey V. Tsiganov
\paper On the Poisson Structures for the Nonholonomic Chaplygin and Veselova Problems
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 439--450
\mathnet{http://mi.mathnet.ru/rcd414}
\crossref{https://doi.org/10.1134/S1560354712050061}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989516}
\zmath{https://zbmath.org/?q=an:1263.37074}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..439T}
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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