Rotation,collapse, and scattering of point vortices

Relative equilibria, collapse, and scattering of point vortices in the plane are studied. Vortex systems with arbitrary choice of circulations are considered. An ordinary differential equation satisfied by polynomials with roots at the vortex positions is found. Explicit expressions for vortex double-ring configurations in the cases of two regular polygons, three regular polygons, and a quadrangle with a digon are obtained.