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

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.

22 pages; 4 figures

References in corpus (4)

• Motion of a circular cylinder and n point vortices in a perfect fluid
• The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices
• The Dynamics of a Rigid Body in Potential Flow with Circulation
• The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

Cited by in corpus (3)

• Fermi-like acceleration and power-law energy growth in nonholonomic systems
• On a Lagrangian reduction and a deformation of completely integrable systems
• The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation