This paper concentrates on four key tools for performing star cluster
simulations developed during the last decade which are sufficient to handle all
the relevant dynamical aspects. First we discuss briefly the Hermite
integration scheme which is simple to use and highly efficient for advancing
the single particles. The main numerical challenge is in dealing with weakly
and strongly perturbed hard binaries. A new treatment of the classical
Kustaanheimo-Stiefel two-body regularization has proved to be more accurate for
studying binaries than previous algorithms based on divided differences or
Hermite integration. This formulation employs a Taylor series expansion
combined with the Stumpff functions, still with one force evaluation per step,
which gives exact solutions for unperturbed motion and is at least comparable
to the polynomial methods for large perturbations. Strong interactions between
hard binaries and single stars or other binaries are studied by chain
regularization which ensures a non-biased outcome for chaotic motions. A new
semi-analytical stability criterion for hierarchical systems has been adopted
and the long-term effects on the inner binary are now treated by averaging
techniques for cases of interest. These modifications describe consistent
changes of the orbital variables due to large Kozai cycles and tidal
dissipation. The range of astrophysical processes which can now be considered
by N-body simulations include tidal capture, circularization, mass transfer by
Roche-lobe overflow as well as physical collisions, where the masses and radii
of individual stars are modelled by synthetic stellar evolution.Comment: Accepted by Cel. Mech. Dyn. Astron., 12 pages including figur
