Variational Principles for Compressible and Incompressible Systems
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چکیده
Some of the results of a previous paper 1 on the relations between adiabatic and incompressible systems are the establishing of a variational energy principle for incompressible systems and consequently of comparison theorems for stability of adiabatic and incompressible perturbations of the same equilibrium state. In this paper we extend these analyses to the most general compressible regimes which are consistent with the variational technique (Hermiticity condition). Moreover, we extend the treatment to the case of anisotropic pressure in the last section. For a uniform fluid which is adiabatically disturbed we have for the square of the oscillation frequency co2 = c 2 / ( d i v ? ) 2 d r / A 2 d r (1)
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