Energy principles for self-gravitating barotropic flows. I - General theory

Details Energy principles for self-gravitating barotropic flows. I - General theory Energy principles for self-gravitating barotropic flows. I - General theory

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993pasj...45..421k&link_type=abstract

PASJ: Publications of the Astronomical Society of Japan (ISSN 0004-6264), vol. 45, no. 3, p. 421-430.

Statistics

Computation

8

Barotropic Flow, Computational Astrophysics, Gravitational Effects, Dynamical Systems, Euler Equations Of Motion, Flow Stability, Perturbation Theory, Steady Flow, Variational Principles

Scientific paper

A principle of minimum energy which is a powerful substitute to the dynamical perturbation method is applied to self-gravitating barotropic flows. A new set of Lagrangian functions is used to prove energy principles for steady motions. With three independent Lagrangian functions, the total energy is stationary for all small variations about a flow with fixed linear and angular momenta, provided that Euler's equations for steady motions are satisfied. Thus steady flows are stable if their energy is minimum. It is concluded that the principle of minimum energy gives stability conditions that are both necessary and sufficient if the terms linear in time derivatives are absent from the Lagrangian.

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