Abstract
A family of polynomial coupled function of n degree is proposed, in order to generalize the Levi-Civita regularization method, in the restricted three-body problem. Analytical relationship between polar radii in the physical plane and in the regularized plane are established; similar for polar angles. As a numerical application, trajectories of the test particle using polynomial functions of 2,3,…,8 degree are obtained. For the polynomial of second degree, the Levi-Civita regularization method is found.
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Roman, R., Szücs-Csillik, I. Generalization of Levi-Civita regularization in the restricted three-body problem. Astrophys Space Sci 349, 117–123 (2014). https://doi.org/10.1007/s10509-013-1628-6
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DOI: https://doi.org/10.1007/s10509-013-1628-6