Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 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
Full-text PDF (392 kB) Citations (3)
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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
Received: 12.05.2014
English version:
Moscow University Mechanics Bulletin, 2016, Volume 71, Issue 2, Pages 27–32
DOI: https://doi.org/10.3103/S0027133016020011
Bibliographic databases:
Document Type: Article
UDC: 531.01+531.552+517.925
Language: Russian
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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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