Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 4017 - 4040, Volume 33, Issue 9, September 2013      doi:10.3934/dcds.2013.33.4017

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Yuri N. Fedorov - Department de Matemática Aplicada I, Universitat Politecnica de Catalunya, Barcelona, E-08028, Spain (email)
Luis C. García-Naranjo - Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, Rio Hondo 1, Mexico City, 01000, Mexico (email)
Joris Vankerschaver - Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom (email)

Abstract: We consider the motion of a planar rigid body in a potential two-dimensional flow with a circulation and subject to a certain nonholonomic constraint. This model can be 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.

Keywords:  Nonholonomic mechanics, fluid-body interaction with circulation, Chaplygin sleigh, integrability.
Mathematics Subject Classification:  Primary: 37J60, 74F10; Secondary: 37J35.

Received: January 2012;      Revised: December 2012;      Available Online: March 2013.