A new integrable problem of motion of point vortices on the sphere

Abstract

The dynamics of an antipodal vortex on a sphere (a point vortex plus its antipode with opposite circulation) is considered. It is shown that the system of n antipodal vortices can be reduced by four dimensions (two degrees of freedom). The cases n = 2, 3 are explored in greater detail both analytically and numerically. We discuss Thomson, collinear and isosceles configurations of antipodal vortices and study their bifurcations. © 2008 Springer.