  We consider the motion of a planar rigid body in a potential flow with
circulation and subject to a certain nonholonomic constraint. This model is
related to the design of underwater vehicles.
  The equations of motion admit a reduction to a 2-dimensional nonlinear
system, which is integrated explicitly. We show that the reduced system
comprises both asymptotic and periodic dynamics separated by a critical value
of the energy, and give a complete classification of types of the motion. Then
we describe the whole variety of the trajectories of the body on the plane.
