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

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

2012-01-24

arxiv.org/abs/1201.5054v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

25 pages, 7 figures

Scientific paper

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.

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