Answers are grounded in this paper and cite their sources.
We show that a sufficient condition for stability for the spherical modes of a stellar system is that the distribution function F(ε) decrease with the energy ε. For this demonstration we approximate the function F(ε) by a succession of steps corresponding to a multiple "water-bag" model. The total energy is shown to be an absolute minimum: The second variation δW of the energy is always strictly positive and there is no marginal mode.
No takes yet. Share an insight, caveat, or question.
Doremus et al. (1971) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: