Abstract

The stability of self-gravitating, collisionless stellar systems has not been well explored until recently. Since the pioneering work by Henon (1973), significant progress has been made by Soviet investigators. These Soviet works are summarized in a monograph by Fridman and Polyachenko (1977). An extensive study of various kinds of dynamical instabilities of spherical stellar systems in equilibrium models has been recently made by Barnes, Goodman and Hut (1986) for a wide range of generalized stellar dynamic polytropes. One of the main results of these works is that stellar systems having predominantly radial orbits are unstable against the developement of strongly triaxial configuration (called the nonradial instability of the first kind by Barnes et. al.). Large portions of the works on this subject are based on the N-body calculations because of the difficulty in doing analytic approach for selfgravitating systems.

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