Routh Reduction by Stages

Symmetry Integrability and Geometry-Methods and Applications

article

Bavo Langerock¹  Tom Mestdag¹  Joris Vankerschaver¹ 

[1] Department of Mathematics, Ghent University;Belgian Institute for Space Aeronomy;Department of Mathematics, University of California at San Diego

关键词: symplectic reduction;    Routh reduction;    Lagrangian reduction;    reduction by stages;   

DOI  :  10.3842/SIGMA.2011.109

来源: National Academy of Science of Ukraine

【 摘 要 】

This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems and this class has the property that it is closed under Routh reduction; (ii) we construct a transformation relating the magnetic Lagrangian system obtained after two subsequent Routh reductions and the magnetic Lagrangian system obtained after Routh reduction w.r.t. to the full symmetry group.

【 授权许可】

Unknown