Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 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
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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).
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 250, Issue 6, Pages 932–941
DOI: https://doi.org/10.1007/s10958-020-05054-y
Bibliographic databases:
Document Type: Article
UDC: 517.933
MSC: 70G60
Language: Russian
Citation: M. V. Shamolin, “Examples of Integrable Systems with Dissipation on the Tangent Bundles of Multidimensional Spheres”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 150, VINITI, Moscow, 2018, 78–87; J. Math. Sci. (N. Y.), 250:6 (2020), 932–941
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. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 150
\pages 78--87
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into330}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3847621}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 250
\issue 6
\pages 932--941
\crossref{https://doi.org/10.1007/s10958-020-05054-y}
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