1201.5054 (Yuri N. Fedorov et al.)

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

Yuri N. Fedorov, Luis C. García-Naranjo, Joris Vankerschaver

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.

View original: http://arxiv.org/abs/1201.5054