ABSTRACT
This chapter discusses regularisation methods which have proved useful in direct N-body simulations of star cluster dynamics. It considers the Kustaanheimo-Stiefel (KS) method which is used for studying perturbed binaries. Although the standard KS method works very well for large perturbations, it is desirable to obtain more reliable long-term solutions without the use of stabilisation or rectification. Hard binaries in star clusters are usually quite stable and spend much of their time experiencing relatively small perturbations. Occasionally hard binaries combine with a single star or another binary to form long-lived hierarchical structures. Strong interactions between binaries and single stars or other binaries are a characteristic feature of star cluster dynamics. The chapter is concerned with the treatment of compact subsystems by several methods of multiple regularisation. It presents the equations of motion for regularisation in 2D.
