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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, Volume 8, Issue 4, Pages 709–715
DOI: https://doi.org/10.21638/spbu01.2021.416 (Mi vspua84) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MECHANICS

Equilibria and oscillations in a reversible mechanical system

V. N. Tkhai

Institute of Control Sciences of the Russian Academy of Sciences, 65, Profsoyuznaya ul., Moscow, 117997, Russian Federation
Full-text PDF (273 kB) Citations (5)
DOI: https://doi.org/10.21638/spbu01.2021.416
Abstract: The paper investigates symmetric periodic motions (SPM) of reversible mechanical systems. A solution is given to the problem of bilateral continuation of a nondegenerate SPM to the global family of such SPMs. The result is applied to the general case of Euler's problem on a heavy rigid body, when the body parameters are not bound by equality conditions and two families of pendulum oscillations are found connecting the lower and upper equilibria.
Keywords: reversible mechanical system, equilibrium, symmetric periodic motion, continuation, global family, Euler's problem, pendulum oscillations.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00146
This work is supported by Russian Foundation for Basic Research (grant no. 19-01-00146).
Received: 28.03.2021
Revised: 02.06.2021
Accepted: 17.07.2021
English version:
Vestnik St. Petersburg University, Mathematics, 2021, Volume 8, Issue 4, Pages 447–451
DOI: https://doi.org/10.1134/S1063454121040191
Document Type: Article
UDC: 517.93:531.36
MSC: 70H33, 34C25, 70E17
Language: Russian
Citation: V. N. Tkhai, “Equilibria and oscillations in a reversible mechanical system”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:4 (2021), 709–715; Vestn. St. Petersbg. Univ., Math., 8:4 (2021), 447–451
Citation in format AMSBIB
\Bibitem{Tkh21}
\by V.~N.~Tkhai
\paper Equilibria and oscillations in a reversible mechanical system
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2021
\vol 8
\issue 4
\pages 709--715
\mathnet{http://mi.mathnet.ru/vspua84}
\crossref{https://doi.org/10.21638/spbu01.2021.416}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2021
\vol 8
\issue 4
\pages 447--451
\crossref{https://doi.org/10.1134/S1063454121040191}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
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