Higher Order Variational Integrators: a polynomial approach
| Autor: | Cédric M. Campos |
|---|---|
| Přispěvatelé: | Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]) |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Polynomial
010102 general mathematics Mathematical analysis [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Type (model theory) Optimal control Symplectic representation Computer Science::Numerical Analysis 01 natural sciences Mathematics::Numerical Analysis 010101 applied mathematics Applied mathematics Symplectic integrator 0101 mathematics Galerkin method Variational integrator Mathematics::Symplectic Geometry Mathematics Symplectic geometry |
| Zdroj: | Advances in Differential Equations and Applications Advances in Differential Equations and Applications, 4, pp.249-258, 2014, SEMA SIMAI Springer Series, 978-3-319-06952-4. ⟨10.1007/978-3-319-06953-1_24⟩ Advances in Differential Equations and Applications ISBN: 9783319069524 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⟩ |
| DOI: | 10.1007/978-3-319-06953-1_24⟩ |
| Popis: | 12 pages, 1 table, 23rd Congress on Differential Equations and Applications, CEDYA 2013; International audience; 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|