  We consider a geometric framework for analytical mechanics with external
forces. Four versions of this framework are considered. A variational principle
with boundary terms and external forces.The second and the third versions are
the Lagrangian and Hamiltonian formulations,respectively. The last one is the
Poisson formulation. An extensive introductory section presents some well known
and some little known geometric constructions to put our formulation in the
appropriate setting to make the comparison of the different formulations
easier.
