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arXiv · 1109.3210

Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation

Luis C. García-Naranjo·Joris Vankerschaver
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Abstract

We consider nonholonomic systems whose configuration space is the central extension of a Lie group and have left invariant kinetic energy and constraints. We study the structure of the associated Euler-Poincare-Suslov equations and show that there is a one-to-one correspondence between invariant measures on the original group and on the extended group. Our results are applied to the hydrodynamic Chaplygin sleigh, that is, a planar rigid body that moves in a potential flow subject to a nonholonomic constraint modeling a fin or keel attached to the body, in the case where there is circulation around the body.

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Luis C. García-Naranjo, Joris Vankerschaver. 2011-09-14. Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation. https://doi.org/10.1016/j.geomphys.2013.05.002

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