Symmetries, constants of the motion, and reduction of mechanical systems with external forces
Abstract
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 socalled 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.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 April 2021
 DOI:
 10.1063/5.0045073
 arXiv:
 arXiv:2101.09036
 Bibcode:
 2021JMP....62d2901D
 Keywords:

 Mathematical Physics;
 Mathematics  Symplectic Geometry;
 Physics  Classical Physics;
 53Z05;
 70F40;
 70H33
 EPrint:
 29 pages, submitted to J. Math. Phys