In the theory of self-gravitating fluid configurations, an important development is related to the discovery that general-relativistic effects of gravitational radiation reaction induce secular instability at certain nonaxisymmetric points of bifurcation along Newtonian sequences of axisymmetric rotating equilibria. Such a point of bifurcation is a point of neutral stability. The present investigation has the objective to develop a new method for isolating nonaxisymmetric bifurcation points. The basis is a derivation of an 'Eulerian' variational principle for neutral, or zero-frequency, nonaxisymmetric modes of oscillation of axisymmetric configurations. The equations governing fluid configurations are discussed, taking into account the equations governing the unperturbed axisymmetric equilibrium configuration, and the equations governing the perturbed configuration. Attention is given to the variational principle, the method for locating Dedekind bifurcation points, and Dedekind and Jacobi bar modes of uniformly rotating configurations.
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Ipser et al. (1985) studied this question.