English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We analyze stability conditions of "Maclaurin flows" (self-gravitating,barotropic, two dimensional, stationary streams moving in closed loops around apoint) by minimizing their energy, subject to fixing all the constants of themotion including mass and circulations. Necessary and sufficient conditions ofstability are obtained when gyroscopic terms in the perturbed Lagrangian arezero. To illustrate and check the properties of this new energy principle, wehave calculated the stability limits of an ordinary Maclaurin disk whosedynamical stability limits are known. Perturbations are in the plane of thedisk. We find all necessary and sufficient conditions of stability for singlemode symmetrical or antisymmetrical perturbations. The limits of stability areidentical with those given by a dynamical analysis. Regarding mixed types ofperturbations the maximally constrained energy principle give for some thenecessary and sufficient condition of stability, for others only sufficientconditions of stability. The application of the new energy principle toMaclaurin disks shows the method to be as powerful as the method of dynamicalperturbations.Comment: (Tex, 36 pages. 3 figures upon request

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