Mathematics
Scientific paper
Sep 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974apj...192..731c&link_type=abstract
Astrophysical Journal, vol. 192, Sept. 15, 1974, pt. 1, p. 731-746.
Mathematics
4
Ellipsoids, Equilibrium Equations, Hydrodynamic Equations, Relativity, Deformation, Gravitational Effects, Inertial Reference Systems, Newton Theory, Rotation, Singularity (Mathematics), Velocity Distribution
Scientific paper
The effects of general relativity, in the post-Newtonian approximation, on the Dedekind figures of equilibrium of homogeneous masses are determined. It is shown how the post-Newtonian figures can be obtained by first altering the velocity field in the Dedekind ellipsoid appropriately, and then subjecting it to a suitable Lagrangian displacement cubic in the coordinates. The solution exhibits a singularity at a point where the axes of the Dedekind ellipsoid are in the ratios 1:0.6158:0.4412. However, in contrast to what happens along the Jacobian sequence, the occurrence of the singularity along the Dedekind sequence is not associated with the onset of any instability at that point by a strict Newtonian-like dynamic perturbation.
Chandrasekhar Subrahmanyan
Elbert Donna D.
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