Variational order for forced Lagrangian systems

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.

References in corpus (5)

• The principle of stationary nonconservative action for classical mechanics and field theories
• High order variational integrators in the optimal control of mechanical systems
• The Case for a Low Mass Black Hole in the Low Mass X-ray Binary V1408 Aquilae (= 4U 1957+115)
• Slimplectic Integrators: Variational Integrators for General Nonconservative Systems
• On the exact discrete Lagrangian function for variational integrators: theory and applications

Cited by in corpus (6)

• Contact variational integrators
• Error analysis of forced discrete mechanical systems
• Variational approach to nonholonomic and inequality-constrained mechanics
• Variational order for forced Lagrangian systems II: Euler-Poincaré equations with forcing
• Lagrangian reduction of forced discrete mechanical systems
• Superconvergence of Galerkin variational integrators