Constructing the Hamiltonian from the behaviour of a dynamical system by proper symplectic decomposition - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

Constructing the Hamiltonian from the behaviour of a dynamical system by proper symplectic decomposition

Résumé

The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the Hamiltonian is not the sum of the potential and kinetic energies. On this ground, we want to address the following problem: data being given in the form of one or more structural evolutions, we want to construct an approximation of the Hamiltonian from a covariant snapshot matrix and to perform a symplectic decomposition. We prove the convergence properties of the method when the time discretization is refined. If the data cloud is not enough rich, we extract the principal component of the Hamiltonian corresponding to the leading modes, allowing to perform a model order reduction for very high dimension models. The method is illustrated by a numerical example.
Fichier principal
Vignette du fichier
GSI2021DeSaxce8PagesPaper.pdf (133.18 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03204511 , version 1 (21-04-2021)

Identifiants

Citer

Nima Shirafkan, Pierre Gosselet, Franz Bamer, Abdelbacet Oueslati, Bernd Markert, et al.. Constructing the Hamiltonian from the behaviour of a dynamical system by proper symplectic decomposition. 5th conference on Geometric Science of Information, Jul 2021, Paris, France. ⟨hal-03204511⟩
51 Consultations
38 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More