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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 2, Pages 185–197
DOI: https://doi.org/10.1134/S1560354714020038 (Mi rcd124) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the Lie Integrability Theorem for the Chaplygin Ball

Andrey V.  Tsiganov

St.Petersburg State University, ul. Ulyanovskaya 1, St. Petersburg, 198504 Russia
Citations (6)
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DOI: https://doi.org/10.1134/S1560354714020038
Abstract: The necessary number of commuting vector fields for the Chaplygin ball in the absolute space is constructed. We propose to get these vector fields in the framework of the Poisson geometry similar to Hamiltonian mechanics.
Keywords: nonholonomic dynamical system, Poisson bracket, Lie theorem, Chaplygin ball.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00061_а
This work was partially supported by RFBR grant 13-01-00061.
Received: 04.12.2013
Accepted: 09.01.2014
Bibliographic databases:
Document Type: Article
MSC: 37J60, 37J35, 70E18, 53D17
Language: English
Citation: Andrey V. Tsiganov, “On the Lie Integrability Theorem for the Chaplygin Ball”, Regul. Chaotic Dyn., 19:2 (2014), 185–197
Citation in format AMSBIB
\Bibitem{Tsi14}
\by Andrey~V. ~Tsiganov
\paper On the Lie Integrability Theorem for the Chaplygin Ball
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 2
\pages 185--197
\mathnet{http://mi.mathnet.ru/rcd124}
\crossref{https://doi.org/10.1134/S1560354714020038}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3189256}
\zmath{https://zbmath.org/?q=an:1335.37046}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000334198000003}
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  • https://www.mathnet.ru/eng/rcd124
  • https://www.mathnet.ru/eng/rcd/v19/i2/p185
    • This publication is cited in the following 6 articles:
    1. Andrey V. Tsiganov, “Hamiltonization and Separation of Variables for a Chaplygin Ball on a Rotating Plane”, Regul. Chaotic Dyn., 24:2 (2019), 171–186  mathnet  crossref
    2. Kurt M. Ehlers, Jair Koiller, “Cartan meets Chaplygin”, Theor. Appl. Mech., 46:1 (2019), 15–46  mathnet  crossref
    3. Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Dynamics and Control of an Omniwheel Vehicle”, Regul. Chaotic Dyn., 20:2 (2015), 153–172  mathnet  crossref  mathscinet  zmath  adsnasa
    4. Andrey V. Tsiganov, “On Integrable Perturbations of Some Nonholonomic Systems”, SIGMA, 11 (2015), 085, 19 pp.  mathnet  crossref
    5. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Hamiltonization of elementary nonholonomic systems”, Russ. J. Math. Phys., 22:4 (2015), 444–453  crossref  mathscinet  zmath  isi  scopus
    6. A. Tsiganov, “Poisson structures for two nonholonomic systems with partially reduced symmetries”, J. Geom. Mech., 6:3 (2014), 417–440  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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