A restricted four-body model for the dynamics near the Lagrangian points of the Sun-Jupiter system
Frederic Gabern - Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (email)
We focus on the dynamics of a small particle near the Lagrangian
points of the Sun-Jupiter system. To try to account for the effect of Saturn,
we develop a specific model based on the computation of a true solution of
the planar three-body problem for Sun, Jupiter and Saturn, close to the real
motion of these three bodies. Then, we can write the equations of motion
of a fourth infinitesimal particle moving under the attraction of these three
masses. Using suitable coordinates, the model is written as a time-dependent
perturbation of the well-known spatial Restricted Three-Body Problem.
Keywords: Trojan asteroids, normal forms, first integrals, invariant tori.
Revised: January 2001; Published: February 2001.
2011 Impact Factor.921