Introduction

The main purpose of this book is to provide algorithms for direct N-body simulations, based on personal experience over many years. A brief description of the early history is included for general interest. We concentrate on developments relating to collisional direct integration methods but exclude three- and four-body scattering, which will be discussed in a separate chapter. In the subsequent section, we introduce some basic concepts which help to understand the behaviour of self-gravitating systems. The topics covered include two-body relaxation, violent relaxation, equipartition of kinetic energy and escape. Although the emphasis is on collisional dynamics, some of the theory applies in the large-N limit that is now being approached with modern hardware and improved numerical techniques. After these theoretical considerations, we turn to the problem at hand and introduce the general principles of direct integration as a beginner's exercise and also describe the first N-body method.

Historical developments

Numerical investigations of the classical N-body problem in the modern spirit can be said to have started with the pioneering effort of von Hoerner [1960]. Computational facilities at that time were quite primitive and it needed an act of faith to undertake such an uncertain enterprise. Looking back at these early results through eyes of experience, one can see that the characteristic features of binary formation and escape are already present for particle numbers as small as N = 16, later increased to 25 [von Hoerner, 1963].