Title: 
SOLAR SYSTEM MODELS WITH A SELECTED SET OF FREQUENCIES

Authors:
G. G\'OMEZ: IEEC & Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain.
e-mail: gerard@maia.ub.es

J. MASDEMONT: IEEC & Departament de Matematica Aplicada I, Universitat
Politecnica de Catalunya, E.T.S.E.I.B., Diagonal 647, 08028 Barcelona, 
Spain. e-mail: josep@barquins.upc.es

J.M. MONDELO: Departament de Matematica Aplicada I, Universitat
Politecnica de Catalunya, E.T.S.E.I.B., Diagonal 647, 08028 Barcelona, 
Spain. e-mail: mondelo@vilma.upc.es

Abstract:

The purpose of this paper is to develop a methodology to generate
simplified models suitable for the analysis of the motion of a small
particle, such as a spacecraft or an asteroid, in the Solar System. The
procedure is based on applying refined Fourier analysis methods to the
time--dependent functions that appear in the differential equations of the
problem.  The equations of the models obtained are quasi--periodic
perturbations of the Restricted Three Body Problem that depend explicitly
on natural frequencies of the Solar System.  Some examples of these new
models are given and compared with other ones found in the literature. For
one of these new models, close to the Earth--Moon system, we have computed the
dynamical substitutes of the collinear libration points.

The methodology developed in this paper can also be used for the analytical
construction of simplified models of systems governed by differential
equations which have a quasi--periodic (in time) external excitation and
such that the form of the equations is rather cumbersome.