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

JOURNAL OF GEOMETRY AND PHYSICS

卷:73

Article

Garcia-Naranjo, Luis C.^1,2  Vankerschaver, Joris^3,4 

[1] IIMAS UNAM, Dept Matemat & Mecan, Mexico City 01000, DF, Mexico

[2] Univ Politecn Cataluna, Dept Matemat Aplicada 1, E-08028 Barcelona, Spain

[3] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[4] Univ Ghent, Dept Math, B-9000 Ghent, Belgium

关键词: Nonholonomic constraints;    Invariant measures;    Central extensions;    Hydrodynamics;   

DOI  :  10.1016/j.geomphys.2013.05.002

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free