Dynamics of autonomous systems with external forces

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.