Nonlinear evolution of spherical stellar systems

A universal method is proposed for the computer simulation of collisionless model systems conforming to a specified distribution function. Calculations are made for various realizations of the model, and the method is applied to show that the growth of instabilities in a spherically symmetric system whose members have nearly radial trajectories, will develop a distinctly ellipsoidal deformation. The method can also be used to construct initial states for any integrable system or systems with equilibrium potentials that admit a complete separation of variables in the conventional sense.