A General Criterion for the Dynamical Stability of Anisotropic Newtonian Systems

TL;DR

This paper introduces a general stability criterion for anisotropic Newtonian systems based on the adiabatic local index, applicable across various physical contexts and capable of identifying configurations that are unstable in isotropic regimes but stable when anisotropic.

Contribution

It proposes a novel, broadly applicable criterion for the dynamical stability of anisotropic systems using the adiabatic local index, expanding the understanding of stability conditions.

Findings

The criterion is valid for multiple physical situations.

Anisotropic configurations can exist where isotropic ones cannot.

Applications demonstrate the criterion's usefulness.

Abstract

The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations. Configurations that cannot exist in the isotropic regime can exist in the anisotropic one. Some applications of the criterion are also included.