A rotating system, such as a star, liquid drop, or atomic nucleus, may rotate as an oblate spheroid about its symmetry axis or, if the angular velocity is greater than a critical value, as a triaxial ellipsoid about a principal axis. The oblate and triaxial equilibrium configurations minimize the total energy, the sum of the rotational kinetic energy plus the potential energy. For a star or galaxy the potential is the self-gravitating potential, for a liquid drop, the surface tension energy, and for a nucleus, the potential is the sum of the repulsive Coulomb energy plus the attractive surface energy. A simple, but accurate, Padé approximation to the potential function is used for the energy minimization problem that permits closed analytic expressions to be derived. In particular, the critical deformation and angular velocity for bifurcation from MacLaurin spheroids to Jacobi ellipsoids is determined analytically in the approximation.
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December 1998
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December 01 1998
Triaxial bifurcations of rapidly rotating spheroids
Ts. Dankova;
Ts. Dankova
Physics Department, Tulane University, New Orleans, Louisiana 70118
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G. Rosensteel
G. Rosensteel
Physics Department, Tulane University, New Orleans, Louisiana 70118
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Am. J. Phys. 66, 1095–1100 (1998)
Article history
Received:
January 12 1998
Accepted:
April 29 1998
Citation
Ts. Dankova, G. Rosensteel; Triaxial bifurcations of rapidly rotating spheroids. Am. J. Phys. 1 December 1998; 66 (12): 1095–1100. https://doi.org/10.1119/1.19050
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