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    Irina Ostrovskaya

    Mil’chakova 8a, Rostov-on-Don, 344090, Russia
    Southern Federal University, Faculty of Mathematics, Mechanics and Computer Sciences


    Kurakin L. G., Ostrovskaya I. V.
    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
    Citation: Kurakin L. G., Ostrovskaya I. V.,  The stability criterion of a regular vortex pentagon outside a circle, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 2, pp.  355-368

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