Introduction

A large number of algorithms are connected with regularization. Many of these concern the KS treatment which plays a key role in the N-body simulation codes. In this chapter, we derive some expressions relating to the conversion of regularized time, followed by other considerations of a practical nature. A separate section provides essential details of the Stumpff KS method as employed in an N-body code. This is followed by an algorithmic discussion of KS termination. Next we describe decision-making procedures for unperturbed two-body motion which speed up the calculation by a large factor. Another important feature with the same objective is the so-called ‘slow-down device’, where the principle of adiabatic invariance is exploited. The theory was given previously in connection with chain regularization and here we discuss the KS implementation. Special treatments of stable hierarchies also contribute significantly to enhanced efficiency while retaining the essential dynamics. Finally, the last sections deal with several processes relating to tidal interactions in close binaries that are connected through an evolutionary sequence. We discuss tidal circularization and two-body capture, as well as Roche-lobe mass transfer which all contribute to making star cluster modelling such an exciting and challenging project.

General KS considerations

We first discuss various general features that are applicable to all the KS methods and also include some aspects of the divided difference scheme, while the next section deals specifically with the Stumpff version.