Higher Order Variational Integrators: a polynomial approach

Abstract : We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the structural properties of these systems, like the symplectic form, the evolution of the momentum maps or the energy behaviour. Also they are easily applicable to optimal control problems based on mechanical systems as proposed in Ober-Bl\"obaum et al. [2011]. Following the same approach, we develop a family of variational integrators to which we refer as symplectic Galerkin schemes in contrast to symplectic partitioned Runge-Kutta. These two families of integrators are, in principle and by construction, different one from the other. Furthermore, the symplectic Galerkin family can as easily be applied in optimal control problems, for which Campos et al. [2012b] is a particular case.
Document type :
Book sections
Liste complète des métadonnées

https://hal.inria.fr/hal-01122917
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, March 4, 2015 - 6:25:07 PM
Last modification on : Friday, April 5, 2019 - 8:21:07 PM
Document(s) archivé(s) le : Friday, June 5, 2015 - 11:20:24 AM

File

1307.6139v1.pdf
Files produced by the author(s)

Identifiers

Citation

Cédric M. Campos. Higher Order Variational Integrators: a polynomial approach. Advances in Differential Equations and Applications, pp.249-258, 2014, SEMA SIMAI Springer Series, 978-3-319-06952-4. ⟨10.1007/978-3-319-06953-1_24⟩. ⟨hal-01122917⟩

Share

Metrics

Record views

235

Files downloads

151