Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978a%26a....62..355s&link_type=abstract
Astronomy and Astrophysics, vol. 62, no. 3, Jan. 1978, p. 355-363, 365-374.
Astronomy and Astrophysics
Astrophysics
13
Adiabatic Flow, Calculus Of Variations, Eigenvalues, Fluid Flow, Gravitational Effects, Perturbation Theory, Eigenvectors, Rayleigh-Ritz Method, Series Expansion, Stellar Structure, Variational Principles
Scientific paper
A perturbational-variational Rayleigh-Ritz (PV-RR) expansion scheme is developed for systematically obtaining the normal modes of small oscillations of self-gravitating fluids in perturbed configurations in powers of an external perturbing parameter that characterizes the eigenvalue equation. Some properties of the generalized perturbed eigenvalue equation are reviewed, a Rayleigh-Ritz ansatz for the eigendisplacements is introduced, and a concise matrix formulation is developed. Appropriate expressions are derived for the PV-RR expansions of the eigenvalues and the eigendisplacement vectors to arbitrarily high perturbation orders. The normal (g and p) modes of a nonadiabatic fluid are then expanded about those of an adiabatic structure. The procedure of Silverman and Sobouti (1977) is used to obtain a series expansion of the eigenfrequencies and eigendisplacements. This procedure is also extended to incorporate the bispectral (g and p) nature of the normal modes into the formalism.
Silverman J. N.
Sobouti Yousef
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