The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of   circulation
  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. 
Yuri N. Fedorov, Luis C. Garc\'ia-Naranjo, Joris Vankerschaver
nlin.SI math-ph math.MP