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.
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 №14.A37.21.1935).
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
\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}
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\zmath{https://zbmath.org/?q=an:1286.70008}
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