Computational studies of the classical gravitational N-body problem have demonstrated the importance in bound systems of energetic binaries formed dynamically. Since analytic and some numerical studies generally neglect three-body interactions, by which these form, it is desirable to establish what role they play in the evolution of a system.

Many wide pairs are to be expected, and theoretical results on their properties, such as the distribution of eccentricities, are confirmed by the results of numerical experiments, but their dynamical importance is slight. Without a detailed consideration of encounters, it seems impossible to predict the numbers of close pairs, which must be time-dependent, and ·special rate functions are introduced to describe the evolution of the distribution of their binding energies. While constraints may be laid on these on general grounds, approximate solutions of the three-body problem are generally required in their evaluation.

Encounters with a wide pair are impulsive, and a reasonably complete theory is possible. Regularised equations of motion facilitate a theory of wide encounters with close pairs and show that the eccentricity distribution relaxes much more rapidly than that of energy, but otherwise only rough results are available. "Exchange" events may occur, or a bound triple system may form, these being treated by a statistical mechanical argument. Many of the results are confirmed hy specially designed nurnerically experiments, using regularisation.

If a cluster contains few close pairs initially, binary evolution is forced by that of the cluster as a whole under collisional relaxation, although the inevitable development of energetic pairs is accompanied by the ejection of fast escapers. Encounters have had little disruptive effect on binaries in the Galaxy within its lifetime. If binaries are formed in similar abundance in clusters, their evolution could force that of the cluster. Systems with a large initial population of binaries deserve further study.