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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 1, Pages 136–146
DOI: https://doi.org/10.1134/S1560354716010081 (Mi rcd58) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Dynamics of the Chaplygin Sleigh on a Cylinder

Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
Citations (13)
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DOI: https://doi.org/10.1134/S1560354716010081
Abstract: This paper is concerned with the motion of the Chaplygin sleigh on the surface of a circular cylinder. In the case of inertial motion, the problem reduces to the study of the dynamical system on a (two-dimensional) torus and to the classification of singular points. Particular cases in which the system admits an invariant measure are found.
In the case of a balanced and dynamically symmetric Chaplygin sleigh moving in a gravitational field it is shown that on the average the system has no drift along the vertical.
Keywords: Chaplygin sleigh, invariant measure, nonholonomic mechanics.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Scientific Foundation (project No. 14-50-00005).
Received: 16.10.2015
Accepted: 28.12.2015
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37C10
Language: English
Citation: Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Dynamics of the Chaplygin Sleigh on a Cylinder”, Regul. Chaotic Dyn., 21:1 (2016), 136–146
Citation in format AMSBIB
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\by Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
\paper Dynamics of the Chaplygin Sleigh on a Cylinder
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 1
\pages 136--146
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    This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:60
     
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