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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2020, Volume 174, Pages 52–69 (Mi into568)  

Odd-order integrable dynamical systems with dissipation

M. V. Shamolin

Lomonosov Moscow State University

Abstract: In this paper, we prove the integrability of some classes of odd-order dynamical systems (namely, systems of order 3, 5, and 7), which are homogeneous in some variables and contain a system on the tangent bundle of a smooth manifolds. In this case, we separate force fields into internal (conservative) and external, which has sign-alternating dissipation. External fields are introduced by using some unimodular transformations and generalize fields considered earlier.

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

DOI: https://doi.org/10.36535/0233-6723-2020-174-52-69

Full text: PDF file (323 kB)
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Bibliographic databases:

UDC: 517.933
MSC: 70G60

Citation: M. V. Shamolin, “Odd-order integrable dynamical systems with dissipation”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 174, VINITI, Moscow, 2020, 52–69

Citation in format AMSBIB
\Bibitem{Sha20}
\by M.~V.~Shamolin
\paper Odd-order integrable dynamical systems with dissipation
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 174
\pages 52--69
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into568}
\crossref{https://doi.org/10.36535/0233-6723-2020-174-52-69}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4150661}


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