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 110–118 (Mi into332)  
Examples of Integrable Systems with Dissipation on the Tangent Bundles of Three-Dimensional Manifolds

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics
Full-text PDF (175 kB) English version article
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Abstract: In this paper, we prove the integrability of certain classes of dynamical systems on the tangent bundles of three-dimensional manifolds (systems with three degrees of freedom). Force field considered possess so-called variable dissipation; they are generalizations of fields studied earlier.
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 964–972
DOI: https://doi.org/10.1007/s10958-020-05055-x
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 Three-Dimensional Manifolds”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 150, VINITI, Moscow, 2018, 110–118; J. Math. Sci. (N. Y.), 250:6 (2020), 964–972
Citation in format AMSBIB
\Bibitem{Sha18}
\by M.~V.~Shamolin
\paper Examples of Integrable Systems with Dissipation on the Tangent Bundles of Three-Dimensional Manifolds
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 150
\pages 110--118
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into332}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3847623}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 250
\issue 6
\pages 964--972
\crossref{https://doi.org/10.1007/s10958-020-05055-x}
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