Geometric numerical methods for mechanics

P Carré (1) , J Bensoam (1)

1 IRCAM - Institut de Recherche et Coordination Acoustique/Musique

In this paper, two classes of numerical integrators are introduced and compared : Lie group methods, presented via the particular case of Runge-Kutta Munthe-Kaas integrators ; and variational methods, in which natural charts integrators and Galerkin methods are examined. Considering the case of a configuration manifold with a Lie group action, both classes of methods are studied in terms of configuration space preservation and symplectic/energy behaviour. As an example, we apply those formulations on the rigid body problem.

Mots clés: Geometric integrators; Structure Preserving numerical methods; Variational methods

Domaines: Systèmes dynamiques [math.DS]; Analyse numérique [math.NA]

P Carré, J Bensoam. Geometric numerical methods for mechanics. Congrès Français de Mécanique, Aug 2019, Brest, France. ⟨hal-02479633⟩