Variational order for forced Lagrangian systems II: Euler-Poincaré equations with forcing
arXiv:1906.09819 · doi:10.1088/1361-6544/ab8bb1
Abstract
In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others. Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the previous construction to the formal derivation of the variational error for numerical integrators of forced Euler-Poincaré equations and the application of this theory to the derivation of geometric integrators for forced systems.
arXiv comment34 pages, 5 figures
References in corpus (7)
- Multisymplectic geometry, variational integrators, and nonlinear PDEs
- The classical mechanics of non-conservative systems
- Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
- Discrete Euler-Poincaré and Lie-Poisson Equations
- Discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids
- Momentum and energy preserving integrators for nonholonomic dynamics
- Variational order for forced Lagrangian systems