Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, Number 2, Pages 25–30 (Mi vmumm132)  

This article is cited in 3 scientific papers (total in 3 papers)

Mechanics

Integrable systems in dynamics on a tangent foliation to a sphere

M. V. Shamolin

Lomonosov Moscow State University, Institute of Mechanics

Abstract: The mechanical systems which have the tangent bundle of a two-dimensional sphere as their phase space are studied. The potential nonconservative systems describing a geodesic flow are classified. A multi-parameter family of systems possessing the complete list of (in general) transcendental first integrals expressed in terms of finite combinations of elementary functions is found. Some examples from spatial dynamics of a rigid body interacting with a medium are given.

Key words: variable dissipation system, dynamic equations, integrability, transcendental first integral.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00848-а


Full text: PDF file (392 kB)
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English version:
Moscow University Mechanics Bulletin, 2016, 71:2, 27–32

Bibliographic databases:

UDC: 531.01+531.552+517.925
Received: 12.05.2014

Citation: M. V. Shamolin, “Integrable systems in dynamics on a tangent foliation to a sphere”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2016, no. 2, 25–30; Moscow University Mechanics Bulletin, 71:2 (2016), 27–32

Citation in format AMSBIB
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\issue 2
\pages 25--30
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Shamolin, “Sluchai integriruemykh sistem s dissipatsiei na kasatelnom rassloenii mnogomernoi sfery”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 150, VINITI RAN, M., 2018, 78–87  mathnet  mathscinet
    2. M. V. Shamolin, “Integrable dynamical systems with dissipation on tangent bundles of 2D and 3D manifolds”, J. Math. Sci. (N. Y.), 244:2 (2020), 335–355  mathnet  crossref  elib
    3. M. V. Shamolin, “Sluchai integriruemosti uravnenii dvizheniya pyatimernogo tverdogo tela pri nalichii vnutrennego i vneshnego silovykh polei”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 187, VINITI RAN, M., 2020, 82–118  mathnet  crossref
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