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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 5, Pages 385–396
DOI: https://doi.org/10.1134/S1560354712050024 (Mi rcd410) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Nonlinear Stability Analysis of a Regular Vortex Pentagon Outside a Circle

Leonid G. Kurakinab, Irina V. Ostrovskayaa

a Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences, ul. Mil’chakova 8a, Rostov-on-Don, 344090 Russia
b Southern Mathematical Institute of VSC RAS, ul. Markusa 22, Vladikavkaz, 362027 Russia
Citations (19)
DOI: https://doi.org/10.1134/S1560354712050024
Abstract: A nonlinear stability analysis of the stationary rotation of a system of five identical point vortices lying uniformly on a circle of radius $R_0$ outside a circular domain of radius $R$ is performed. The problem is reduced to the problem of stability of an equilibrium position of a Hamiltonian system with a cyclic variable. The stability of stationary motion is interpreted as Routh stability. Conditions for stability, formal stability and instability are obtained depending on the values of the parameter $q=R^2/R^2_0$.
Keywords: point vortices, stationary motion, stability, resonance.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.A18.21.0873
Russian Foundation for Basic Research 11-05-01138
11-05-91052
10-05-00646
This work was supported by the Ministry of Education and Science of the Russian Federation within the framework of the Federal program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia for the years 2009-2013” (contract No 14.A18.21.0873), and the Russian Foundation for Basic Research (Grants 11-05-01138, 11-05-91052 and 10-05-00646).
Received: 26.01.2012
Accepted: 24.03.2012
Bibliographic databases:
Document Type: Article
MSC: 76B47, 34D20, 70K30
Language: English
Citation: Leonid G. Kurakin, Irina V. Ostrovskaya, “Nonlinear Stability Analysis of a Regular Vortex Pentagon Outside a Circle”, Regul. Chaotic Dyn., 17:5 (2012), 385–396
Citation in format AMSBIB
\Bibitem{KurOst12}
\by Leonid G. Kurakin, Irina V. Ostrovskaya
\paper Nonlinear Stability Analysis of a Regular Vortex Pentagon Outside a Circle
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 5
\pages 385--396
\mathnet{http://mi.mathnet.ru/rcd410}
\crossref{https://doi.org/10.1134/S1560354712050024}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2989512}
\zmath{https://zbmath.org/?q=an:1252.76017}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..385K}
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  • https://www.mathnet.ru/eng/rcd/v17/i5/p385
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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