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

This article is cited in 10 scientific papers (total in 10 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
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).


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Bibliographic databases:

MSC: 70E18, 76B47
Received: 25.11.2011

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
\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

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    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. 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
    5. Yu. L. Karavaev, A. A. Kilin, “Dinamika sferorobota s vnutrennei omnikolesnoi platformoi”, Nelineinaya dinam., 11:1 (2015), 187–204  mathnet  elib
    6. 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
    7. 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
    8. 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
    9. 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
    10. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582  mathnet  crossref  mathscinet
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