Equations for core collapse in clusters

This paper is concerned with core collapse in isolated clusters of identical point masses. Equations are derived which determine the evolution of the core which would result from given deviations from a Maxwellian distribution. Assuming certain forms for the deviations, the predicted evolution of the core is compared with the results of Monte Carlo calculations. The deviations corresponding to stars moving in nearly radial orbits appear ultimately to dominate the evolution of the core. The deviations are maintained because stars of high energy cannot relax fast enough to thermalize with the evolving core. Under certain crude approximations, the deviations for stars in radial orbits can approach a homological form. (author)