  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 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 of Lagrangian systems subjected to external
forces which are invariant under the action of a Lie group.
