Global Regularization of a Restricted Four-Body Problem

In the n-body problem, a collision singularity occurs when the position of two or more bodies coincide. By understanding the dynamics of collision motion in the regularized setting, a better understanding of the dynamics of near-collision motion is achieved. In this paper, we show that any double collision of the planar equilateral restricted four-body problem can be regularized by using a Birkhoff-type transformation. This transformation has the important property to provide a simultaneous regularization of three singularities due to binary collision. We present some ejection–collision orbits after the regularization of the restricted four-body problem (RFBP) with equal masses, which were obtained by numerical integration.