Nonlinear Stability of Riemann Ellipsoids with Symmetric Configurations

TL;DR

This paper uses geometric methods to determine the conditions under which symmetric Riemann ellipsoids are both existent and nonlinearly stable, advancing understanding of their stability in astrophysical contexts.

Contribution

It provides necessary and sufficient conditions for the existence and nonlinear stability of symmetric Riemann ellipsoids using geometric techniques.

Findings

Derived stability criteria for symmetric Riemann ellipsoids.

Identified conditions for the existence of these ellipsoids.

Enhanced understanding of their nonlinear stability properties.

Abstract

We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Riemann ellipsoids having at least two equal axes.