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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
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.
Received: 26.01.2012 Accepted: 24.03.2012
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
Linking options:
https://www.mathnet.ru/eng/rcd410 https://www.mathnet.ru/eng/rcd/v17/i5/p385
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