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We consider the motion of a planar rigid body in a potential flow withcirculation and subject to a certain nonholonomic constraint. This model isrelated to the design of underwater vehicles.  The equations of motion admit a reduction to a 2-dimensional nonlinearsystem, which is integrated explicitly. We show that the reduced systemcomprises both asymptotic and periodic dynamics separated by a critical valueof the energy, and give a complete classification of types of the motion. Thenwe describe the whole variety of the trajectories of the body on the plane.

The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation