TITLE:
A dynamical study of Hilda asteroids in the Circular and Elliptic RTBP

AUTHORS:
Angel Jorba^(1,2), Bego\~na Nicolas^(3), Oscar Rodriguez^(4)

(1) Departament de Matematiques i Informatica,
    Universitat de Barcelona
(2) Centre de Recerca Matematica (CRM), Barcelona
(3) Departamento de Matematica Aplicada,
    Universidade de Santiago de Compostela
(4) Departament de Matematiques,
    Universitat Politecnica de Catalunya, 

The Hilda group is a set of asteroids whose mean motion is in a 3:2
orbital resonance with Jupiter. In this paper we use the planar
Circular Restricted Three-Body Problem (CRTBP) as a dynamical model
and we show that there exists a family of stable periodic orbits that
are surrounded by islands of quasi-periodic motions.  We have computed
the frequencies of these quasi-periodic motions and we have shown how
the Hilda family fits inside these islands.  We have compared these
results with the ones obtained using the Elliptic Restricted
Three-Body Problem and they are similar, showing the suitability of
the CRTBP model. It turns out that, to decide if a given asteroid
belongs to the Hilda class, it is much better to look at its
frequencies in the planar CRTBP rather than to use two-body orbital
elements as it is commonly done today.