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arXiv · 2101.09036

Symmetries, constants of the motion and reduction of mechanical systems with external forces

Manuel de León·Manuel Lainz·Asier López-Gordón
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Abstract

This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain a Noether's theorem for Lagrangian systems with external forces, among other results regarding symmetries and conserved quantities. We particularize our results for the so-called Rayleigh dissipation, i.e., external forces that are derived from a dissipation function, and illustrate them with some examples. Moreover, we present a theory for the reduction of Lagrangian systems subjected to external forces which are invariant under the action of a Lie group.

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Manuel de León, Manuel Lainz, Asier López-Gordón. 2021-01-22. Symmetries, constants of the motion and reduction of mechanical systems with external forces. https://doi.org/10.1063/5.0045073

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