  The purpose of this paper is to perform an error analysis of the variational
integrators of mechanical systems subject to external forcing. Essentially, we
prove that when a discretization of contact order $r$ of the Lagrangian and
force are used, the integrator has the same contact order. Our analysis is
performed first for discrete forced mechanical systems defined over $TQ$, where
we study the existence of flows, the construction and properties of discrete
exact systems and the contact order of the flows (variational integrators) in
terms of the contact order of the original systems. Then we use those results
to derive the corresponding analysis for the analogous forced systems defined
over $Q\times Q$.
