Introduction

We describe some relevant algorithms for initializing and terminating higher-order systems which are selected for the merger treatment discussed in chapter 11. Such configurations may consist of a single particle or binary in bound orbit around an existing triple or quadruple, or be composed of two stable triples. There are some significant differences from the standard case, the main one being that the KS solution of the binary is not terminated at the initialization. In other words, the complexity of the structure is increased, and the whole process is reminiscent of molecular chemistry. However, once formed as a KS solution, the new hierarchy needs to be restored to its original constituents at the termination which is usually triggered by large perturbations or mass loss. Special procedures are also required for removing all the relevant components of escaping hierarchies, and here we include merged triples and quadruples since the treatment is similar to that for higher-order systems.

Initialization

Consider an existing hierarchy of arbitrary multiplicity and mass, mi, which is to be merged with the mass-point mj, representing any object in the form of a single particle or even another hierarchy. Again we adopt the convention of denoting the component masses of a KS pair by mk and ml, respectively. Some of the essential steps are listed in Algorithm C.1.

Nearly all of these steps also appear in the standard case and therefore do not require comment. We note one important difference here, in that there is no termination of the KS solution.