A new set of integrals of motion to propagate the perturbed two-body problem

A formulation of the perturbed two-body problem that relies on a new set of orbital elements is presented. The proposed method represents a generalization of the special perturbation method published by Peláez et al. (Celest Mech Dyn Astron 97(2):131?150,2007) for the case of a perturbing force that is partially or totally derivable from a potential. We accomplish this result by employing a generalized Sundman time transformation in the framework of the projective decomposition, which is a known approach for transforming the two-body problem into a set of linear and regular differential equations of motion. Numerical tests, carried out with examples extensively used in the literature, show the remarkable improvement of the performance of the new method for different kinds of perturbations and eccentricities. In particular, one notable result is that the quadratic dependence of the position error on the time-like argument exhibited by Peláez?s method for near-circular motion under the J2 perturbation is transformed into linear.Moreover, themethod reveals to be competitive with two very popular elementmethods derived from theKustaanheimo-Stiefel and Sperling-Burdet regularizations

Levi-Civita,Tullio

International audienceTullio Levi-Civita (29 March 1873 to 29 December 1941) has been an Italian mathematician and mathematical physicist, known above all for his work on the absolute differential calculus. Levi-Civita came from a rigorous and creative school of mathematical physicists and was a pupil of Gregorio Ricci-Curbastro. LeviCivita’s work included outstanding results in pure and applied mathematics and in celestial and analytic mechanics but also celebrated textbooks. These last, even those written in Italian, have influenced mathematical physicists all over the world.Levi-Civita has perfected some conceptual tools of great importance in modern science, particularly in general relativity, number theory, and continuum mechanics