Integration of the long term rotation for celestial bodies (Timothée Vaillant, Paris)

06.02.2018 14:00

The celestial bodies in the Solar System present an orbital motion around the Sun and a rotational motion. The equations of these two motions are coupled but they can present periods of different orders of magnitude. The rotational motion present a proper rotation whose period for the different bodies of the Solar System can vary between a few hours for the fast rotators and a hundred days for the slow rotators.

We will present how the symplectic integration of these equations can be realized according to the rotation period. For the fast rotators, an average on the proper rotation can be performed to obtain integration schemes analogous to Farago et al. (2009). For the slow rotators, the integration of the Hamiltonian of the free rigid body can be realized by symplectic integrators (McLachlan 1993, Touma and Wisdom 1994, Reich 1994). We will see in particular that the features of the Lie algebra of the angular momentum can allow to obtain more effective integrators which are specific to the free rigid body. These symplectic integrators must present coefficients, which depend on the moments of inertia of the integrated body.

Lieu

salle 623, Séminaire d'analyse numérique

Organisé par

Section de mathématiques

Intervenant-e-s

Timothée Vaillant , Observatoire de Paris

entrée libre

Classement

Catégorie: Séminaire

Mots clés: analyse numérique