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Russian Mathematical Surveys, 2014, Volume 69, Issue 3, Pages 481–538
DOI: https://doi.org/10.1070/RM2014v069n03ABEH004899 (Mi rm9587) 		 
This article is cited in 27 scientific papers (total in 27 papers)

Non-holonomic dynamics and Poisson geometry

A. V. Borisova, I. S. Mamaevab, A. V. Tsiganovc

a Udmurt State University, Izhevsk
b Izhevsk State Technical University
c Saint Petersburg State University
English version PDF (925 kB) Citations (27) Russian version article
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DOI: https://doi.org/10.1070/RM2014v069n03ABEH004899
Abstract: This is a survey of basic facts presently known about non-linear Poisson structures in the analysis of integrable systems in non-holonomic mechanics. It is shown that by using the theory of Poisson deformations it is possible to reduce various non-holonomic systems to dynamical systems on well-understood phase spaces equipped with linear Lie–Poisson brackets. As a result, not only can different non-holonomic systems be compared, but also fairly advanced methods of Poisson geometry and topology can be used for investigating them.
Bibliography: 95 titles.
Keywords: non-holonomic systems, Poisson bracket, Chaplygin ball, Suslov system, Veselova system.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Science Foundation 14-19-01303
The research of the first author was carried out in the framework of the state contract "Regular and Chaotic Dynamics" with Udmurt State University. The research of the second author was supported by grant no. 14-19-01303 of the Russian Science Foundation ("Dynamics and Control of Mobile Robototechnological Systems").
Received: 23.12.2013
Bibliographic databases:
Document Type: Article
UDC: 514.853+517.925+531.38+531.012
MSC: Primary 70F25, 70G45; Secondary 53D17
Language: English
Original paper language: Russian
Citation: A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538
Citation in format AMSBIB
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\by A.~V.~Borisov, I.~S.~Mamaev, A.~V.~Tsiganov
\paper Non-holonomic dynamics and Poisson geometry
\jour Russian Math. Surveys
\yr 2014
\vol 69
\issue 3
\pages 481--538
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    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:875
    Russian version PDF:325
    English version PDF:46
    References:102
    First page:53
     
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