Abstract
A method is described for creating a distribution function for an anisotropic nearly spherical dissipationless gravitational system that originates from a cold collapse and is relaxed close to an equilibrium state. The method is based on taking advantage of several regularities that appear in the numerical data of N-body experiments. In particular, a two-dimensional histogram of the number density of particles N(E, L 2 ) on a plane of energy E and square angular momentum L 2 is constructed and the shapes of equidensity contours studied. An analytic formula is obtained that gives a very good fit to N(E, L 2 ) throughout the domain of the histogram. The radial period T r (E, L 2 ) is found to depend almost entirely on the energy, being independent of angular momentum apart from a small variation of less than 1 per cent
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