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Regul. Chaotic Dyn., 2013, Volume 18, Issue 5, Pages 490–496 (Mi rcd133)  

This article is cited in 8 scientific papers (total in 8 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

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).


DOI: https://doi.org/10.1134/S156035471305002X

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Bibliographic databases:

Document Type: Article
MSC: 70E18, 76B47
Received: 25.11.2011
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://www.ams.org/mathscinet-getitem?mr=3117257}
\zmath{https://zbmath.org/?q=an:1286.70008}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325810200002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    2. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213  mathnet  crossref  mathscinet  zmath
    3. Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “Special Solutions of a High-order Equation for Waves in a Liquid with Gas Bubbles”, Regul. Chaotic Dyn., 19:5 (2014), 576–585  mathnet  crossref  mathscinet  zmath
    4. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
    5. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “The Jacobi Integral in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 20:3 (2015), 383–400  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    6. Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    7. Alexander P. Ivanov, “On the Control of a Robot Ball Using Two Omniwheels”, Regul. Chaotic Dyn., 20:4 (2015), 441–448  mathnet  crossref  mathscinet  zmath  adsnasa  elib
    8. 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
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