Nonlinear velocities in generalized Riemann ellipsoids.

Physics

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Stellar Systems: Stability, Stellar Systems: Equilibrium Figures

Scientific paper

The Dirichlet problem concerning the equilibrium conditions, under which a self-gravitating homogeneous fluid mass can maintain at every instant an ellipsoidal form, is generalized. The authors provide the conditions necessary to solve the Dirichlet problem in a more general case of heterogeneous masses having nonlinear internal motions, using the second-order virial equations. The conditions for the stability are presented. It is also proved that the Dedekind theorem generalized to these new solutions is valid. These models may lead to a direct explanation of some basic features of galactic morphology.

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