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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 2, Pages 191–198
DOI: https://doi.org/10.1134/S1560354712020074 (Mi rcd339) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Two Non-holonomic Integrable Problems Tracing Back to Chaplygin

Alexey V. Borisov, Ivan S. Mamaev

Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
Citations (23)
DOI: https://doi.org/10.1134/S1560354712020074
Abstract: The paper considers two new integrable systems which go back to Chaplygin. The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange’s gyroscope. All necessary first integrals and an invariant measure are found. The solutions are shown to be expressed in terms of quadratures.
Keywords: non-holonomic constraint, integrability, invariant measure, gyroscope, quadrature, coupled rigid bodies.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 11.G34.31.0039
02.740.11.0195
14.740.11.0876
This research was supported by the Grant of the Government of the Russian Federation for state support of scientific research conducted under supervision of leading scientists in Russian educational institutions of higher professional education (contract no. 11.G34.31.0039) and the Federal target programme “Scientific and Scientific-Pedagogical Personnel of Innovative Russia”, measure 1.1. “Scientific-Educational Center Regular and Chaotic Dynamics” (project code 02.740.11.0195), measure 1.5 “Topology and Mechanics” (project code 14.740.11.0876).
Received: 14.08.2011
Accepted: 29.11.2011
Bibliographic databases:
Document Type: Article
MSC: 76M23, 34A05
Language: English
Citation: Alexey V. Borisov, Ivan S. Mamaev, “Two Non-holonomic Integrable Problems Tracing Back to Chaplygin”, Regul. Chaotic Dyn., 17:2 (2012), 191–198
Citation in format AMSBIB
\Bibitem{BorMam12}
\by Alexey V.~Borisov, Ivan S.~Mamaev
\paper Two Non-holonomic Integrable Problems Tracing Back to Chaplygin
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 2
\pages 191--198
\mathnet{http://mi.mathnet.ru/rcd339}
\crossref{https://doi.org/10.1134/S1560354712020074}
\zmath{https://zbmath.org/?q=an:1252.76056}
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  • https://www.mathnet.ru/eng/rcd/v17/i2/p191
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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