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Stability of Relative Equilibria of Point Vortices on a Sphere and Symplectic Integrators

By Jerrold E. Marsden, Sergey Pekarsky and Steve Shkoller


This paper analyzes 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 provided for the (integrable) case N = 3. Stabilityof relative equilibria is analyzed bythe energy-momentum method. Explicit criteria for stabilityof different configurations with generic and non-generic momenta are obtained. In each case, a group of transformations is specified, such that motion in the original (unreduced) phase space is stable modulo this group. Finally, we outline the construction of a symplectic-momentum integrator for vortex dynamics on a sphere

Topics: c ○ Società Italiana di Fisica 1
Year: 1999
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