Variational order for forced Lagrangian systems
This work offers a theoretical foundation for constructing high-order numerical integrators for forced Lagrangian/Hamiltonian systems, which is relevant for computational mechanics and physics simulations.
The authors extend the variational framework for forced mechanical systems by duplicating variables, enabling the design of high-order integrators and providing a characterization of the order of methods for forced systems via the variational order of the duplicated system.
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.