Relative Equilibria of the (1+N)-Vortex Problem
نویسندگان
چکیده
منابع مشابه
Stability of Relative Equilibria in the Planar n-Vortex Problem
We study the linear and nonlinear stability of relative equilibria in the planar n-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological approach is taken to show that for the case of positive circulations, a relative equilibrium is linearly stable if and only if it is a nondegenerate minimum...
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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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Helmholtz’s equations provide the motion of a system of N vortices which describes a planar incompressible fluid. A relative equilibrium is a particular solution of these equations for which the distances between the particles are invariant during the motion. In this article, we are interested in relative equilibria formed of concentric regular polygons of vortices. We show that in the case of ...
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15 صفحه اولRelative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
We examine in detail the relative equilibria in the planar four-vortex problem where two pairs of vortices have equal strength, that is, Γ1 = Γ2 = 1 and Γ3 = Γ4 = m where m ∈ R−{0} is a parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapez...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Science
سال: 2011
ISSN: 0938-8974,1432-1467
DOI: 10.1007/s00332-011-9108-z