Four-vortex motion with zero total circulation and impulse

The problem of four interacting point vortices on the unbounded plane with vanishing total circulation and vanishing impulse is reduced to a three-bod y problem analogous to the three-vortex problem on the unbounded plane. A " phase plane analysis" using trilinear coordinates, similar to that used for the three-vortex problem, is presented and used to discuss details of the motion. The methodology and results complement earlier analyses of the same problem by Eckhardt and Rott. (C) 1999 American Institute of Physics. [S10 70-6631(99)01912-1].