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Katz, Lynda J.; Feroz, Ray

doi:10.1007/978-1-4899-0694-6_17

Cited by 1 publication

(1 citation statement)

References 66 publications

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“…The main purpose of this work is to illustrate on a test case our principle of "maximally constrained" energy minimum (Katz, Inagaki and Yahalom 1993), and find stability limits of stationnary motions of barotropic flows. Paper I dealt with three dimensional flows and gave no application.…”

Section: Introductionmentioning

confidence: 99%

Energy principles for self-gravitating barotropic flows - II. The stability of Maclaurin discs

Yahalom¹,

Katz²,

Inagaki

1994

Monthly Notices of the Royal Astronomical Society

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We analyze stability conditions of "Maclaurin flows" (self-gravitating, barotropic, two dimensional, stationary streams moving in closed loops around a point) by minimizing their energy, subject to fixing all the constants of the motion including mass and circulations.Necessary and sufficient conditions of stability are obtained when gyroscopic terms in the perturbed Lagrangian are zero. To illustrate and check the properties of this new energy principle, we have calculated the stability limits of an ordinary Maclaurin disk whose dynamical stability limits are known. Perturbations are in the plane of the disk. We find all necessary and sufficient conditions of stability for single mode symmetrical or antisymmetrical perturbations. The limits of stability are identical with those given by a dynamical analysis. Regarding mixed types of perturbations the maximally constrained energy principle give for some the necessary and sufficient condition of stability, for others only sufficient conditions of stability. The application of the new energy principle to Maclaurin disks shows the method to be as powerful as the method of dynamical perturbations.

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Section: Introductionmentioning

confidence: 99%