Perturbative solution of the motion of an asteroid in resonance with Jupiter

Using a new technique, we derive general formulae for the rate of change of orbital parameters of an asteroid with negligible mass, perturbed by a mas sive planet (such as Jupiter) having a commensurable period. The relative s trength of the perturbing force defines the perturbation parameter, but our results are also expanded in terms of both eccentricities (of the perturbi ng and the perturbed body) and the mutual inclination. This approach can se rve as a valuable tool in the ongoing study of the so-called stable chaos, and may facilitate its ultimate explanation.