On the Szebehely / Bond Equation - Generalized Sundman's Transformation for the Perturbed Two-Body Problem

In this paper, starting with the Szebehely and Bond (1983) equation, we rediscuss the regularization and linearization of the perturbed planar two-body problem. We study the generalization of the Sundman's (1912) transformation proposed by Szebehely and Bond and obtain the radial and transverse perturbations (represented by powers of the radial distance r), which can be linearized with these transformations. In this way we generalize some previous results of Belen'kii (1981a, b) and Szebehely and Bond (1983). We also consider another generalization of Sundman's transformation, introduced by Cid et al. (1983), in the case when the radial and transverse perturbations are presented by polynomials in the reciprocal of the distance. As a consequence we give a partial answer to a problem suggested by Szebehely and Bond (1983).