THE VIRIAL TENSOR AND ITS APPLICATION TO SELF-GRAVITATING FLUIDS

Journal Article · Fri Sep 01 04:00:00 EDT 1961 · Astrophysical Journal (U.S.)

DOI:https://doi.org/10.1086/147175· OSTI ID:4833422

Lebovitz, N R

The well-known conditions for the Maclaurin spheroids and and the Jacobi ellipsoids are found as consequences of the tensor virial equations. The perturbation forms of the tensor virial equations are derived- and applied th the stability of the self-gravitating sphere, the Maclaurin spheroids, and the Jacobi ellipsoids. The effect of rotation on the oscillation frequencies of a self- gravitating sphere is found in dethil for second-order harmonic deformations of the equilib rium shape. To first order in the angular speed OMEGA , the five oscillation frequencies associated with the five secondorder harmonics are sigma /sub 0/ yields sigma , OMEGA /sub 0/0 - 1/2 OMEGA , sigma /sub 0/0, sigma / sub 0/ + 1/2 OMEGA , and sigma /sub 0/ + OMEGA , where sigma /sub 0/ is the Kelvin frequency of the non-rotating spherical liquid mass. Two critical values of the eccentricity are found for the Maclaurin spheroids. The first, e = 0.8127, marks the point where the series of Maclaurin spheroids has a member in commion with the Jacobi ellipsoids. The second, e = 0.9529, is the place where the Maclaurin spheroids become unstable. The effect of certain special perturbations of the Maclaurin spheroids with these values of the eccentricity is discussed. (auth)

• Research Organization: Yerkes Observatory, Williams Bay, Wis.
• NSA Number: NSA-15-031364
• OSTI ID: 4833422
• Journal Information: Astrophysical Journal (U.S.), Journal Name: Astrophysical Journal (U.S.) Vol. Vol: 134; ISSN ASJOA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

EQUATIONS
FLUIDS
FOURIER ANALYSIS
FREQUENCY
GRAVITATION
HARMONIC ANALYSIS
MASS
MATHEMATICS
OSCILLATIONS
PERTURBATION THEORY
PHYSICS
ROTATION
STABILITY
TENSORS
VECTORS