# 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…

## 7 Citations

Hybrid Routhian reduction for simple hybrid forced Lagrangian systems

- Engineering2022 European Control Conference (ECC)
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This paper discusses Routh reduction for simple hybrid forced mechanical systems. We give general conditions on whether it is possible to perform symmetry reduction for a simple hybrid Lagrangian…

Nonsmooth Herglotz variational principle

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—In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular,…

Symplectic and Cosymplectic Reduction for simple hybrid forced mechanical systems with symmetries

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This paper gives general conditions on whether it is possible to perform symmetry reduction for simple hybrid Hamiltonian and Lagrangian systems subject to non-conservative external forces, as well as time-dependent external forces.

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A discrete version of systems with Rayleigh-type forces is introduced, the equations of motion are obtained and the equivalence is characterized, and a Hamilton-Jacobi theory for forced discrete Hamiltonian systems is developed.

Geometric Hamilton–Jacobi theory for systems with external forces

- MathematicsJournal of Mathematical Physics
- 2022

In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples.…

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The work done by Isaac Newton more than three hundred years ago, continues being a path to increase our knowledge of Nature. To better understand all the ideas behind it, one of the finest ways is to…

The geometry of Rayleigh dissipation

- Mathematics
- 2021

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…

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