Phase-space structure of the Buckingham’s two-body problem

In this paper, we study the global flow for the two-body problem associated to the Buckingham potential. For this, using McGehee-type transformations, we write the regularized equations of motion. Then, reducing the 4-dimensional phase space to a 2-dimension one, the global flow in the phase plane is described for all possible values of the parameters of the potential and those of the energy and angular momentum constants. Every phase trajectory is interpreted in terms of physical motion, our problem being depicted both geometrically and physically.