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arXiv · 0802.0146

Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations

T. Mestdag·M. Crampin
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Abstract

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory.

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T. Mestdag, M. Crampin. 2008-02-01. Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations. https://doi.org/10.1088/1751-8113%2F41%2F34%2F344015

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