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, 2022, Volume 209, Pages 88–107
DOI: https://doi.org/10.36535/0233-6723-2022-209-88-107
(Mi into1006)
 

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

Systems with dissipation with five degrees of freedom: Analysis and integrability. II. Dynamical systems on tangent bundles

M. V. Shamolin

Lomonosov Moscow State University
Full-text PDF (303 kB) Citations (6)
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Abstract: The work contains the second and third parts of the survey on the integrability of systems with five degrees of freedom (the first part: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 208, (2022), pp. 91–121). In the first part, the primordial problem from the dynamics of a multidimensional rigid body placed in a nonconservative force field was described in detail. In the second and third parts, we consider more general dynamical systems on tangent bundles to the five-dimensional sphere and other smooth manifolds of a sufficiently wide class. Theorems on sufficient conditions for the integrability of the considered dynamical systems in the class of transcendental functions are proved.
Keywords: dynamical system with five degrees of freedom, 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: 517.9; 531.01
MSC: 34Cxx, 70Cxx
Language: Russian
Citation: M. V. Shamolin, “Systems with dissipation with five degrees of freedom: Analysis and integrability. II. Dynamical systems on tangent bundles”,  Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 209, VINITI, Moscow, 2022, 88–107
Citation in format AMSBIB
\Bibitem{Sha22}
\by M.~V.~Shamolin
\paper Systems with~dissipation with~five degrees of freedom: Analysis and integrability. II. Dynamical systems on tangent bundles
\inbook  Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2022
\vol 209
\pages 88--107
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1006}
\crossref{https://doi.org/10.36535/0233-6723-2022-209-88-107}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    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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