The pulsations and the dynamical stability of gaseous masses in uniform rotation

Abstract

A variational principle, applicable to axisymmetric oscillations of uniformly rotating axisymmetric configurations, is established On the assumption that the Lagrangian displacement (describing the oscillation) at any point is normal to the level surface (of constant total potential) through that point, it is shown how the variational expression, for the frequencies of oscillation, can be reduced to simple quadratures. The reduction is explicitly carried out for certain stratifications of special interest. Some new results on the oscillations of slowly rotating configurations are included; and a number of related observations on their stability are also made.