A Qualitative Analysis of a Joint Dynamics of Kirchhoff and a Point Vortices

The integrable problem of a joint motion of a point vortex and the Kirchhoff one is considered. The reduction of the system is carried out in algebraic variables. The phase portrait of the system is constructed, the points of relative equilibrium are investigated. The solutions relevant to elliptic fixed points are found in absolute coordinates. Nonintegrability of interaction of a vortex spot with two point vortices is proved for the restricted problem.