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Nelin. Dinam., 2012, Volume 8, Number 2, Pages 355–368 (Mi nd326)  

The stability criterion of a regular vortex pentagon outside a circle

L. G. Kurakinab, I. V. Ostrovskayab

a South Mathematical Institute of VSC RAS, Markusa 22, Vladikavkaz, 362027, Russia
b Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences, Milchakova 8a, Rostov-on-Don, 344090, Russia

Abstract: The nonlinear stability analysis of a stationary rotation of a system of five identical point vortices lying uniform on a circle of radius $R_0$ outside a circular domain of radius $R$ is performed. The problem is reduced to the problem of equilibrium of Hamiltonian system with cyclic variable. The stability of stationary motion is interpreted as Routh stability. The conditions of stability, formal stability and instability are obtained subject to the parameter $q=R^2/R_0^2$.

Keywords: point vortices, stationary rotation, stability, resonance

Full text: PDF file (461 kB)
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UDC: 532.517
MSC: 76B47, 34D20, 70K30
Received: 26.01.2012
Accepted:24.03.2012

Citation: L. G. Kurakin, I. V. Ostrovskaya, “The stability criterion of a regular vortex pentagon outside a circle”, Nelin. Dinam., 8:2 (2012), 355–368

Citation in format AMSBIB
\Bibitem{KurOst12}
\by L.~G.~Kurakin, I.~V.~Ostrovskaya
\paper The stability criterion of a regular vortex pentagon outside a circle
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 2
\pages 355--368
\mathnet{http://mi.mathnet.ru/nd326}


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