  This paper discusses reduction by symmetries for autonomous and
non-autonomous forced mechanical systems with inelastic collisions. In
particular, we introduce the notion of generalized hybrid momentum map and
hybrid constants of the motion to give general conditions on whether it is
possible to perform symmetry reduction for Hamiltonian and Lagrangian systems
subject to non-conservative external forces and non-elastic impacts, as well as
its extension to time-dependent mechanical systems subject to time-dependent
external forces and time-dependent inelastic collisions. We illustrate the
applicability of the method with examples and numerical simulations.
