Variational order for forced Lagrangian systems

TL;DR

This paper develops a variational framework for forced Lagrangian systems, enabling the derivation of equations of motion and the design of high-order integrators, by duplicating system variables as introduced in prior work.

Contribution

It introduces a variational approach for forced systems using variable duplication, providing a new method to analyze and develop integrators with specific order properties.

Findings

Derived equations of motion for forced systems variationally.

Linked variational order to integrator accuracy for forced systems.

Provided a framework for high-order integrator design.

Abstract

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.