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

@article{deLen2021SymmetriesCO,
  title={Symmetries, constants of the motion, and reduction of mechanical systems with external forces},
  author={Manuel de Le{\'o}n and Manuel Lainz and Asier L{\'o}pez-Gord{\'o}n},
  journal={Journal of Mathematical Physics},
  year={2021},
  volume={62},
  pages={042901}
}
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… 
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