Annu. Rev. Astron. Astrophys. 1991. 29: 239-274
Copyright © 1991 by . All rights reserved

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2.3 Separable Models

Certain triaxial potentials admit three exact isolating integrals of motion. These are the potentials for which the Hamilton-Jacobi equation separates in specific orthogonal curvilinear coordinates. Special cases were discussed as long as 150 years ago (see 78 and 106 for historical references). The separable potentials have been named after Stäckel, who was the first to classify them systematically (254, 317, 318). Their appearance in astronomy came through Eddington's seminal work on stellar dynamics (61, 102, 221). The crucial insight that they correspond to smooth inhomogeneous mass models is due to Kuzmin (197, 198). Their orbital structure resembles closely that of triaxial elliptical galaxies, and they are convenient prototypical models for these systems.