Dynamics in the center manifold around equilibrium points periodically perturbed three-body problems

Bastien Le Bihan (1) , Josep Masdemont (2) , Gérard Gómez (3) , Stéphanie Lizy-Destrez (4)

1 DISC - Département d'Ingénierie des Systèmes Complexes
2 UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona]
3 UB - Universitat de Barcelona
4 DCAS - Département Conception et conduite des véhicules Aéronautiques et Spatiaux

A new application of the parameterization method is presented to compute invariant manifolds about the equilibrium points of Periodically Perturbed Three-Body Problems (PPTBP). These techniques are applied to obtain high-order semi-numerical approximations of the center manifolds about the points L1,2 of the Sun-perturbed Earth-Moon Quasi-Bicircular Problem (QBCP), which is a particular case of PPTBP. The quality of these approximations is compared with results obtained using equivalents of previous normal form procedures. Then, the parameterization is used to initialize the computation of Poincaré maps, which allow to get a qualitative description of the periodically-perturbed dynamics near the equilibrium points.

Mots clés: Parameterization method; Center manifold; Four-body model; Quasi-bicircular problem; Sun-Earth; Moon system

Domaines: Astrophysique [astro-ph]

Bastien Le Bihan, Josep Masdemont, Gérard Gómez, Stéphanie Lizy-Destrez. Dynamics in the center manifold around equilibrium points periodically perturbed three-body problems. Proceedings of the International Conference on Antenna Theory and Techniques (ICATT 2016), Mar 2016, Darmstadt, Germany. pp. 1-10. ⟨hal-03200246⟩