A restricted four-body model for the dynamics near the Lagrangian points of the Sun-Jupiter system
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain, Spain
Then, we study the dynamics of this model near the triangular points. The tools are based on computing, up to high order, suitable normal forms and first integrals. From these expansions, it is not difficult to derive approximations to invariant tori (of dimensions 2, 3 and 4) as well as bounds on the speed of diffusion on suitable domains. We have also included some comparisons with the motion of a few Trojan asteroids in the real Solar system.
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