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The Lagrange's planetary equations written in terms of the classical orbital elements have the     disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical     model used and do not have physical reasons. In this paper, we studied the third-body perturbation     using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of     the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate     short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon     or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which     are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity     and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the     inclination

Third-Body Perturbation Using a Single Averaged Model: Application in Nonsingular Variables