Introduction

The basic theory of chain regularization [Mikkola & Aarseth, 1990, 1993] is described in chapter 5, while algorithms that deal with different treatments of physical collisions are detailed in chapter 9. Here we are concerned with a number of additional features that deal with aspects relating to what might be termed the N-body interface, namely how to combine two different solution methods in a consistent way. Strong interactions in compact subsystems are usually of short duration, with the ejection of energetic particles a characteristic feature. First we give some algorithms for unperturbed triple and quadruple systems while the more extensive treatment of perturbed chain regularization is discussed in the subsequent sections. As far as the internal chain subsystem is concerned, this requires extra procedures that add to the program complexity and cost. Having selected a suitable subsystem for special treatment, we also need to consider the change of membership and possible astrophysical processes. Moreover, the question of when to terminate a given configuration requires suitable decision-making for the switch to alternative methods, as well as identification of hierarchical stability in order to prevent inefficiency. Finally, since the implementation of the time-transformed leapfrog scheme has many similarities with chain regularization, we include some relevant algorithms here.