Generalization of Levi-Civita regularization in the restricted three-body problem

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.

Accepted for publication in Astrophysics and Space Science

References in corpus (2)

• Regularization of the circular restricted three-body problem using 'similar' coordinate systems
• `Similar' coordinate systems and the Roche geometry. Application

Cited by in corpus (3)

• Regularization of the restricted $(n+1)$-body problem on curved spaces
• Corrected Newtonian potentials in the two-body problem with applications
• A family of zero-velocity curves in the restricted three-body problem