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Abstract: This paper concerns the Routh reduction procedure for Lagrangians systemswith symmetry. It differs from the existing results on geometric Routhreduction 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 aregular value of $J L$. The main results of this paper are: the description ofa general Routh reduction procedure that preserves the Euler-Lagrange nature ofthe original system and the presentation of a presymplectic framework for Routhreduced systems. In addition, we provide a detailed description andinterpretation of the Euler-Lagrange equations for the reduced system. Theproposed procedure includes Lagrangian systems with a non-positively definitekinetic energy metric.



Author: Bavo Langerock, Marco Castrillón López

Source: https://arxiv.org/







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