Routh Reduction for Singular Lagrangians

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 JL are required apart from the momentum being a regular value of JL. 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 equa-tions for the reduced system. The proposed procedure includes Lagrangian systems with a non-positively definite kinetic energy metric.
Depto. de Álgebra, Geometría y Topología
Fac. de Ciencias Matemáticas
Instituto de Matemática Interdisciplinar (IMI)
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