Stability of relative equilibria of three vortices
نویسندگان
چکیده
منابع مشابه
Point vortices on a sphere: Stability of relative equilibria
In this paper we analyze the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are worked out for the ~integrable! case of three vortices. The system under consideration is SO~3! invariant; the associated momentum map generated by this SO~3! symmetry is equivariant and cor...
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We examine existence and stability of relative equilibria of the nvortex problem specialized to the case where N vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero, the weak vortices tend to a circle centered on the strong vortex. A special potential function of this limiting problem can be used to characterize orbits and stabi...
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The problem of determining relative equilibria of identical point vortices is longstanding. The simplest such equilibria, vortices arranged at the vertices of a regular polygon with or without one at the center, go back to the work by Kelvin and Thomson late in the 19th century, and are wound up with the now defunct theory of vortex atoms. Many years later, Havelock found relative equilibria co...
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We prove the existence of many different symmetry types of relative equilibria for systems of identical point vortices on a non-rotating sphere. The proofs use the rotational symmetry group SO(3) and the resulting conservation laws, the time-reversing reflectional symmetries in O(3), and the finite symmetry group of permutations of identical vortices. Results include both global existence theor...
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The system of point vortices on the sphere is a Hamiltonian system with symmetry SO(3), and there are stable relative equilibria of four point vortices, where three identical point vortices form an equilateral triangle circling a central vortex. These relative equilibria have zero (nongeneric) momentum and form a family that extends to arbitrarily small diameters. Using the energy-momentum meth...
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تاریخ انتشار 2017