A SECULAR INTEGRATOR FOR ASTEROID FRAGMENTS

This work is a byproduct of the proper element program by Lemaitre and Morbidelli (Celest. Mech., submitted, 1993). The Hamiltonian of the p roblem (massless asteroid perturbed by Jupiter and Saturn) is averaged with respect to the mean longitudes of both the asteroid and the plan ets, and is coded in a new grid directly in Arnold action-angle variab les. These are the most suitable ones in order to take into account th e strongly nonlinear dynamics related to the motion of the argument of perihelion, which is dominant at large inclination. Only the three ma in terms, corresponding to the three main secular resonances nu5, nu6 and nu16, are retained in the perturbation. The averaged equations of motion are integrated directly in action-angle variables. Therefore th is secular integrator turns out to be very fast (30 s for 1 million ye ars on a HP710 workstation). However, owing to the simplifications of the model, the results are not quantitatively accurate, albeit preserv ing the main features of the real dynamics. So, this secular integrato r is very suitable for statistical studies on the behaviour of thousan ds of fictitious objects, such as simulated fragments of real asteroid s, in order to study the dynamical mechanisms of meteorite transport.