Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898566 | Journal of Geometry and Physics | 2013 | 14 Pages |
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–Poincaré–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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Luis C. García-Naranjo, Joris Vankerschaver,