Perturbations and stability of rotating stars. II - Properties of the eigenvectors and a variational principle. III - Perturbation theory for eigenvalues

Details Perturbations and stability of rotating stars. II - Properties of the eigenvectors and a variational principle. III - Perturbation theory for eigenvalues Perturbations and stability of rotating stars. II - Properties of the eigenvectors and a variational principle. III - Perturbation theory for eigenvalues

Jan 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980mnras.190....7s&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 190, Jan. 1980, p. 7-31.

Astronomy and Astrophysics

Astrophysics

14

Dynamic Stability, Eigenvectors, Ideal Fluids, Perturbation Theory, Stellar Models, Stellar Rotation, Variational Principles, Astrophysics, Eigenvalues, Jordan Form, Operators (Mathematics), Orthogonality, Rotating Fluids, Stellar Gravitation, Symmetry

Scientific paper

The paper considers properties of the normal modes of linear pulsation of perfect-fluid rotating stars, restricting it to finite-dimensional versions of the problem. It is shown that stars which have the time-azimuth reflection symmetry in their unperturbed state have the property that any right-eigenvalue can be changed into the adjoint of the left-eigenvector for the same eigenvalue; this permits a variational principle for the eigenfrequencies of all the normal modes to be formulated.

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