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

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