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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 150, Pages 78–87 (Mi into330)  

Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: In this paper, we prove the integrability of certain classes of dynamical systems that appear in the dynamics of multidimensional rigid bodies and the dynamics of a particle moving on a multidimensional sphere. Force field considered have the so-called variable dissipation with zero mean; they are generalizations of fields studied earlier. We present examples of the application of the method for integrating dissipative systems on the tangent bundles of two-dimensional surfaces of revolution.

Keywords: dynamical system, nonconservative force field, integrability, transcendental first integral

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00848-a
This work was partially supported by the Russian Foundation for Basic Research (project No. 15-01-00848-a).


Full text: PDF file (188 kB)

Bibliographic databases:

Document Type: Article
UDC: 517.933
MSC: 70G60

Citation: M. V. Shamolin, “Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 150, VINITI, Moscow, 2018, 78–87

Citation in format AMSBIB
\Bibitem{Sha18}
\by M.~V.~Shamolin
\paper Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 150
\pages 78--87
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into330}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3847621}


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