On the energy method in the stellar stability problem

Details On the energy method in the stellar stability problem On the energy method in the stellar stability problem

Feb 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979a%26a....72...55k&link_type=abstract

Astronomy and Astrophysics, vol. 72, no. 1-2, Feb. 1979, p. 55-60.

Astronomy and Astrophysics

Astrophysics

5

Dynamic Stability, Energy Methods, Stellar Models, Boundary Value Problems, Perturbation Theory, Stellar Structure, Variational Principles

Scientific paper

The dynamical stability of stellar models to radial perturbations is investigated on the basis of the energy method. Necessary and sufficient conditions for stability are derived, including stationarity conditions and the nontangency condition, the Legendre S-condition, the Weierstrass S-condition, and the focal-point S-condition. It is shown that the energy method is rigorously equivalent to the usual eigenvalue analysis when applied to small perturbations. The relation between the present results and those obtained previously in the framework of the energy method is considered, along with the relation between the energy and small-perturbation methods. It is concluded that the energy method is rigorously equivalent to the small-perturbation method when applied to infinitesimally neighboring configurations.

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