Regular Algorithms for the Few-Body Problem

encounters of just two bodies. Most classical numerical integration methods lose precision for such situations due to the 1/r² singularity of the mutual force of the two bodies. In a close encounter the relative motion of the participating bodies is so fast that, for a brief moment, the rest of the system can be considered frozen. Consequently, the most important feature of a regularizing algorithm must be that it can handle reliably the perturbed two-body problem. There are two basically different types of methods available: Coordinate and time transformations and algorithms that produce regular results without coordinate transformation.