Triaxial bifurcations of rapidly rotating spheroids

Details Triaxial bifurcations of rapidly rotating spheroids Triaxial bifurcations of rapidly rotating spheroids

1999-09-29

arxiv.org/abs/nucl-th/9909074v1

Am.J.Phys. 66 (1998) 1095

Physics

Nuclear Physics

Nuclear Theory

10 pages, 6 figures

Scientific paper

10.1119/1.19050

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, a 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, Pad\'{e} 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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