DYNAMICAL BEHAVIOUR OF ASTEROIDS IN RESONANCE: FIRST ORDER COMMENSURABILITIES
		Fernandez S.*  and  Lopez Garcia F.**
			ABSTRACT

	The aim of our work is to explore the dynamical behaviour of asteroids
in commensurability or near it by stuying the time evolution of their orbital
elements. We have studied first order commensurabilities with Jupiter,
particularly the 3:2 and 4:3 ones. Our method is based on the numerical
integration of the heliocentric motion equations and the analysis of different
elements. We have used the gravitational hypothesis considering Jupiter as the
main perturbator, i.e. planar elliptic restricted three-body problem and as a
second step we have included the perturbations of Saturn as a fourth body. In
order to consider the possible status of motion according to the initial
conditions we have represented the phase surface (-1/a, phi). This phase plane
allows us to have some idea about the regularity of the asteroidal
behaviour...When the motion is regular but not commensurable, a stripe
parallel to x-axis is obtained. When a commensurabilityof mean motion is
present there are two different behaviours according to the regulariry of
motion: if the distribution of points has a ring-shape the motion is regular
and if it has a non ordered distribution the motion is non regular. We have
integrated fictitious and real asteroids varying the initial conditions for
all of them, mean anomalies M and the other initial parameters. We have found
a strong dependence of these initial conditions on the behaviour of the
asteroids.

* Observatorio Astronomico Cordoba, Argentina
** Observatorio Astronomico Felix Aguilar, Argentina

Note: PHI means the Greek letter