On Equilibrium Figures for Ideal Fluids in the Form of Confocal Ellipsoids Rotating with Common Angular Velocity

Details On Equilibrium Figures for Ideal Fluids in the Form of Confocal Ellipsoids Rotating with Common Angular Velocity On Equilibrium Figures for Ideal Fluids in the Form of Confocal Ellipsoids Rotating with Common Angular Velocity

Jun 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990rmxaa..20...15m&link_type=abstract

Revista Mexicana de Astronomia y Astrofisica, 20,

Astronomy and Astrophysics

Astronomy

3

Scientific paper

RESUMEN Se demuestra la existencia de figuras de equilibrio para un cuerpo fluido, autogravitante y libre de presi6n externa, que consiste de dos elipsoides confocales de distiiita densidad que giran con velocidad angular comun. El analisis muestra que a cada valor asignado a la densidad relativa del cuerpo, le corresponde un solo grado de achatamiento, es decir, no puede existir una sene. Otra conclusi6n es que Ia densidad relativa posee un inferior (tal que la densidad del elipsoide interior es ligeramente mayor que el doble de Ia del exterior) y al respecto se ofrece una explicaci6n semicualitativa. Se asume que el flufdo es ideal e incompresible. ABSTRACT For a self-gravitating free from external pressure fluid body, consisting of two homogeneous Co nfo cal ellipsoids of different density rotating with common angular velocity, we demonstrate the existence of equilibrium figures. No senes is possible, however, since the rotating body attains, for given values of its relative density, a unique degree of flattening. In addition, the analysis shows that there is a lower limit to the relative density (in which case the density of the interior ellipsoid is only slightly larger than twice the density of the exterior one) and a semi-qualitative explanation on the subject is offered. The fluids are assumed ideal and incompressible. Key words: HYDRODYNAMICS

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