Star cluster dynamics: Mathematical models

Each of the three classes of mathematical models which are discussed in this paper, have strengths and weaknesses, which can perhaps be summarised as follows: the N-body model is best for small N, the Fokker-Planck equation is best for big N, while the fluid model yields the quickest but least trustworthy results. The use of supercomputers will have the most important consequences for the first two models, but there is little prospect as yet that the N-body model will supplant the Fokker-Planck model for the treatment of large systems like globular clusters. The time step needed would correspond to a few minutes, in order to compute the orbits of tidal binaries with sufficient accuracy, while the total integration time would correspond to more than 10/sup 10/ years; a ratio of more than 10/sup 14/. It is this range of time scales which is perhaps the greatest obstacle to the application of N-body methods, and even hybrid schemes, to the dynamics of large star clusters