Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2014, Number 4, Pages 43–50 (Mi vmumm335)  
This article is cited in 4 scientific papers (total in 4 papers)

Mechanics

Steady and periodic modes in the problem of motion of a heavy material point on a rotating sphere (the viscous friction case)

E. S. Shalimova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (544 kB) Citations (4)
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Abstract: The problem of motion of a heavy material point on a sphere uniformly rotating about a fixed axis is considered in the case of viscous friction. The angle of inclination between the axis and the horizon is constant. The existence, bifurcation, and stability of the equilibrium positions are discussed. The existence of periodic motions is also studied. An approach is proposed to find such motions in the case of low viscosity.
Key words: viscous friction, motion of a particle on a sphere, positions of equilibrium, periodic modes.
Funding agency Grant number
Russian Foundation for Basic Research 12-08-00591
12-08-00637
Ministry of Education and Science of the Russian Federation 14.B37.21.0225
Received: 05.04.2013
English version:
Moscow University Mechanics Bulletin, 2014, Volume 69, Issue 4, Pages 89–96
DOI: https://doi.org/10.3103/S0027133014040025
Bibliographic databases:
Document Type: Article
UDC: 531.36
Language: Russian
Citation: E. S. Shalimova, “Steady and periodic modes in the problem of motion of a heavy material point on a rotating sphere (the viscous friction case)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 4, 43–50; Moscow University Mechanics Bulletin, 69:4 (2014), 89–96
Citation in format AMSBIB
\Bibitem{Sha14}
\by E.~S.~Shalimova
\paper Steady and periodic modes in the problem of motion of a heavy material point on a rotating sphere (the viscous friction case)
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2014
\issue 4
\pages 43--50
\mathnet{http://mi.mathnet.ru/vmumm335}
\transl
\jour Moscow University Mechanics Bulletin
\yr 2014
\vol 69
\issue 4
\pages 89--96
\crossref{https://doi.org/10.3103/S0027133014040025}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84926666591}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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