Abstract:
The dynamical evolution of a spheroidal cluster of point masses is investigated theoretically, extending the analysis of Som Sunder and Kochhar (1985) by removing the assumption of locally isotropic velocity. The basic equations are derived, and results for the collapse of pressureless systems, systems with negative total energy and nonzero pressure, systems with positive total energy, and heterogeneous spheroids are presented graphically. It is found that the zero-pressure cluster behaves like the pressureless gas clouds studied by Lin et al. (1965), that a negative-energy cluster with pressure undergoes finite-amplitude size and eccentricity oscillations (with amplitude dependent on the initial eccentricity) but does not oscillate between prolate and oblate configurations, and that positive-energy clusters (including heterogeneous clusters) remain prolate or oblate while expanding to dispersion.
