  We are able to derive the equations of motion for forced mechanical systems
in a purely variational setting, both in the context of Lagrangian or
Hamiltonian mechanics, by duplicating the variables of the system as introduced
by Galley [2013], Galley, Tsang, and Stein [2014]. We show that this
construction is useful to design high-order integrators for forced Lagrangian
systems and, more importantly, we give a characterization of the order of a
method applied to a forced system using the corresponding variational order of
the duplicated one.
