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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.: Year: Volume: Issue: Page: Find

 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}