1109.3210 (Luis C. García-Naranjo et al.)

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

Luis C. García-Naranjo, Joris Vankerschaver

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.

View original: http://arxiv.org/abs/1109.3210