On the dynamical evolution of a spheroidal cluster

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Abstract
Tensor virial equations are used to investigate the dynamical evolution of a cluster of mass points characterized by a spheroidal (homogeneous or heterogeneous) distribution of matter and an isotropic distribution of velocities. It is known that if the total energy of the system is positive, it will disperse to infinity. We show that in the case of negative total energy, the system executes finite amplitude oscillations between oblate and prolate shapes.

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