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Regular and Chaotic Dynamics, 2013, Volume 18, Issue 5, Pages 490–496
DOI: https://doi.org/10.1134/S156035471305002X (Mi rcd133) 		 
This article is cited in 11 scientific papers (total in 11 papers)

The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity

Alexey V. Borisovabc, Ivan S. Mamaevcba

a Institute of Computer Science; Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b A. A. Blagonravov Mechanical Engineering Research Institute of RAS, ul. Bardina 4, Moscow, 117334 Russia
c Institute of Mathematics and Mechanics of the Ural Branch of RAS, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
Citations (11)
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DOI: https://doi.org/10.1134/S156035471305002X
Abstract: We consider the problem of rolling of a ball with an ellipsoidal cavity filled with an ideal fluid, which executes a uniform vortex motion, on an absolutely rough plane. We point out the case of existence of an invariant measure and show that there is a particular case of integrability under conditions of axial symmetry.
Keywords: vortex motion, nonholonomic constraint, Chaplygin ball, invariant measure, integrability, rigid body, ideal fluid.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation NSh-2519.2012.1
1.1248.2011
1.7734.2013
14.A37.21.1935
This work was carried out at the Udmurt State University and was supported by Grant of the President of the Russian Federation for Support of Leading Scientific Schools NSh-2519.2012.1 “Dynamical Systems of Classical Mechanics and Control Problems”, Analytic Departmental Target Program “Development of Scientific Potential of Higher Schools” (1.1248.2011), Analytic Depart-mental Target Program “Development of Scientific Potential of Higher Schools” (1.7734.2013), Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” (Agreement ¹14.A37.21.1935).
Received: 25.11.2011
Accepted: 18.01.2012
Bibliographic databases:
Document Type: Article
MSC: 70E18, 76B47
Language: English
Citation: Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity”, Regul. Chaotic Dyn., 18:5 (2013), 490–496
Citation in format AMSBIB
\Bibitem{BorMam13}
\by Alexey V. Borisov, Ivan S. Mamaev
\paper The Dynamics of the Chaplygin Ball with a Fluid-filled Cavity
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 5
\pages 490--496
\mathnet{http://mi.mathnet.ru/rcd133}
\crossref{https://doi.org/10.1134/S156035471305002X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3117257}
\zmath{https://zbmath.org/?q=an:1286.70008}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000325810200002}
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  • https://www.mathnet.ru/eng/rcd/v18/i5/p490
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:51
     
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