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Keywords:

  • chaos;
  • celestial mechanics, stellar dynamics;
  • minor planets, asteroids

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 massive planet (such as Jupiter) having a commensurable period. The relative strength of the perturbing force defines the perturbation parameter, but our results are also expanded in terms of both eccentricities (of the perturbing and the perturbed body) and the mutual inclination. This approach can serve as a valuable tool in the ongoing study of the so-called stable chaos, and may facilitate its ultimate explanation.