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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2022, Volume 205, Pages 55–94
DOI: https://doi.org/10.36535/0233-6723-2022-205-55-94
(Mi into957)
 

This article is cited in 6 scientific papers (total in 6 papers)

Systems with four degrees of freedom with dissipation: analysis and integrability

M. V. Shamolin

Lomonosov Moscow State University
Full-text PDF (429 kB) Citations (6)
References:
Abstract: This paper is a survey on integrable systems with four degrees of freedom whose phase spaces are tangent bundles of four-dimensional smooth manifolds. First, we discuss in detail the original problem from the dynamics of a multidimensional rigid body in a nonconservative force field; then we consider general dynamical systems on the tangent bundles of a sufficiently large class of smooth manifolds and prove sufficient conditions for the integrability of the dynamical systems considered in the class of transcendental.
Keywords: dynamical system, integrability, transcendental first integral.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00016
This work was supported by the Russian Foundation for Basic Research (project No. 19-01-00016).
Document Type: Article
UDC: 517, 531.01
MSC: 34Cxx, 70Cxx
Language: Russian
Citation: M. V. Shamolin, “Systems with four degrees of freedom with dissipation: analysis and integrability”, Geometry and Mechanics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 205, VINITI, Moscow, 2022, 55–94
Citation in format AMSBIB
\Bibitem{Sha22}
\by M.~V.~Shamolin
\paper Systems with four degrees of freedom with dissipation: analysis and integrability
\inbook Geometry and Mechanics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 205
\pages 55--94
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into957}
\crossref{https://doi.org/10.36535/0233-6723-2022-205-55-94}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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    Full-text PDF :60
    References:49
     
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