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arXiv · 1201.5054

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

Yuri N. Fedorov·Luis C. García-Naranjo·Joris Vankerschaver
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Abstract

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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Yuri N. Fedorov, Luis C. García-Naranjo, Joris Vankerschaver. 2012-01-24. The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation. https://doi.org/10.3934/dcds.2013.33.4017

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