  We study the bar instability in collisionless, rotating, anisotropic, stellar
systems, using N-body simulations and also the matrix technique for calculation
of modes with the perturbed collisionless Boltzmann equation. These methods are
applied to spherical systems with an initial Plummer density distribution, but
modified kinematically in two ways: the velocity distribution is tangentially
anisotropic, using results of Dejonghe, and the system is set in rotation by
reversing the velocities of a fraction of stars in various regions of phase
space, a la Lynden-Bell. The aim of the N-body simulations is first to survey
the parameter space, and, using those results, to identify regions of phase
space (by radius and orbital inclination) which have the most important
influence on the bar instability. The matrix method is then used to identify
the resonant interactions in the system which have the greatest effect on the
growth rate of a bar. Complementary series of N-body simulations examine these
processes in relation to the evolving frequency distribution and the pattern
speed. Finally, the results are synthesised with an existing theoretical
framework, and used to consider the old question of constructing a stability
criterion.
