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

This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain Noether’s theorem for Lagrangian systems with external forces, among other results regarding symmetries and conserved quantities. We particularize our results for...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-04, Vol.62 (4)
Main Authors: de León, Manuel, Lainz, Manuel, López-Gordón, Asier
Format: Article
Language:English
Subjects:
Lie groups
Mechanical systems
Physics
Reduction
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Summary:This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain 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 in Lagrangian systems subjected to external forces, which are invariant under the action of a Lie group.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0045073