Nonlinear Stability of Riemann Ellipsoids with Symmetric Configurations

Using modern differential geometric methods, we study the relative equilibria for Dirichlet's model of a self-gravitating fluid mass having at least two equal axes. We show that the only relative equilibria of this type correspond to Riemann ellipsoids for which the angular velocity and vorticity are parallel to the same principal axis of the body configuration. The two solutions found are MacLaurin and transversal spheroids.


Published in:
Journal Of Nonlinear Science, 19, 179-219
Year:
2009
Keywords:
Laboratories:




 Record created 2010-11-30, last modified 2018-01-28


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