On a criterion for the occurrence of a Dedekind-like point of bifurcation along a sequence of axisymmetric systems. II. Newtonian theory for differentially rotating configurations

Abstract

The equations in the Newtonian theory, which govern quasi-stationary nonaxisymmetric deformations of axisymmetric configurations in nonuniform rotation, are derived; and the condition for the existence of such deformations with a Φ-dependence of the form e^imΦ (where m is an integer greater than or equal to 1) is expressed in terms of a variational principle. The condition for the case m=2 applies for the occurrence of a Dedekind-like point of bifurcation. In an appendix the variational principle governing the axisymmetric modes of oscillation of differentially rotating systems is reformulated in a manner that avoids the solution of a second¬order partial differential equation.