TITLE:
The Bianular and Tricircular Coherent Problems.

AUTHORS:
Frederic Gabern and Angel Jorba
Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona,
Gran Via 585, 08007 Barcelona, Spain
E-mails: gabern@mat.ub.es, angel@maia.ub.es

ABSTRACT:
In this paper we construct two models for the motion of a
particle under the gravitational attraction of Sun, Jupiter, Saturn
and Uranus, that can be seen as a generalization of the well known
Restricted Three-Body Problem (RTBP). Both models are obtained by
computing quasi-periodic solutions --with two basic frequencies-- of a
suitable $N$-body problem.
The first model is based on a quasi-periodic solution of the planar
Sun-Jupiter-Saturn Three-Body problem, that tries to approach the real
motion of Jupiter. The second model is based on a quasi-periodic
solution of the Sun-Jupiter-Saturn-Uranus Four-Body problem. In both
cases, we derive the equations of motion for a particle under the
gravitational attraction of these bodies as a quasi-periodic
time-dependent perturbation of the well-known RTBP.