Nonlinear velocities in generalized riemann ellipsoids
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The Dirichlet problem concerning the equilibrium conditions, under which a self-gravitating homogeneous fluid-mass can maintain at every instant an ellipsoidal form, is here generalized. We 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.
PACS95.30 Fundamental aspects of astrophysics
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