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, 2020, Volume 187, Pages 68–81
DOI: https://doi.org/10.36535/0233-6723-2020-187-68-81
(Mi into733)
 

Examples of nine-order integrable dynamical systems with dissipation

M. V. Shamolin

Lomonosov Moscow State University
References:
Abstract: In this paper, the integrability of some classes of homogeneous with respect to a part of variables ninth-order dynamical systems, in which a system on the tangent bundle to four-dimensional manifolds is distinguished. In this case, force fields have a dissipation of different signs and are generalizations of those considered earlier.
Keywords: dynamical system, nonconservative force fields, integrability, transcendental first integral.
English version:
Journal of Mathematical Sciences (New York), 2025, Volume 287, Issue 5, Pages 754–766
DOI: https://doi.org/10.1007/s10958-025-07639-x
Bibliographic databases:
Document Type: Article
UDC: 517, 531.01
MSC: 58-xx, 70-xx
Language: Russian
Citation: M. V. Shamolin, “Examples of nine-order integrable dynamical systems with dissipation”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 187, VINITI, Moscow, 2020, 68–81; J. Math. Sci. (N. Y.), 287:5 (2025), 754–766
Citation in format AMSBIB
\Bibitem{Sha20}
\by M.~V.~Shamolin
\paper Examples of nine-order integrable dynamical systems with dissipation
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 187
\pages 68--81
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into733}
\crossref{https://doi.org/10.36535/0233-6723-2020-187-68-81}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4672037}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2025
\vol 287
\issue 5
\pages 754--766
\crossref{https://doi.org/10.1007/s10958-025-07639-x}
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