Routh reduction for singular Lagrangians

Details Routh reduction for singular Lagrangians Routh reduction for singular Lagrangians

2010-07-02

arxiv.org/abs/1007.0325v1

Physics

Mathematical Physics

34 pages, 2 figures, accepted for publicaton in International Journal of Geometric Methods in Modern Physics (IJGMMP)

Scientific paper

This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian $L$ or the momentum map $J_L$ are required apart from the momentum being a regular value of $J_L$. The main results of this paper are: the description of a general Routh reduction procedure that preserves the Euler-Lagrange nature of the original system and the presentation of a presymplectic framework for Routh reduced systems. In addition, we provide a detailed description and interpretation of the Euler-Lagrange equations for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric.

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