Editing Appendix/Ramblings/TurningPoints (section)

=See Also=

The discussion presented here is supported by detailed reviews and new derivations presented in the following associated chapters: 
* A [[SSC/FreeEnergy/PolytropesEmbedded#Free-Energy_Synopsis| free-energy synopsis]].  
* Material associated with an [[SSC/FreeEnergy/Powerpoint#Supporting_Derivations_for_Free-Energy_PowerPoint_Presentation|overarching PowerPoint presentation]].
* [[SSC/Structure/LimitingMasses#Mass_Upper_Limits|Limiting Masses]]
* An [[SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|accompanying chapter on the Bonnor-Ebert sphere]].

Overlapping discussions of this topic may also be found in the following key references:
* &sect;6.8 of [<b>[[Appendix/References#ST83|<font color="red">ST83</font>]]</b>].

Other publications that are closely aligned with the analysis found in {{ Darwin06full }}:
<ul>
<li>G. H. Darwin (1901, Philosophical Transactions of the Royal Society A, Vol. 197, pp. 461 - 557), ''Ellipsoidal Harmonic Analysis.''</li>
<li>G. H. Darwin (1902, Philosophical Transactions of the Royal Society A, Vol. 198, pp. 301 - 331), ''The Pear-Shaped Figure of Equilibrium of a Rotating Mass of Liquid.''</li>
<li>G. H. Darwin (1903, Philosophical Transactions of the Royal Society A, Vol. 200, pp. 251 - 314), ''The Stability of the Pear-Shaped Figure of Equilibrium, &amp;c.''</li>
<li>G. H. Darwin (1904, Philosophical Transactions of the Royal Society A, Vol. 203, pp. 111 - 137), ''Integrals of the Squares of Ellipsoidal Surface Harmonic Functions.''</li>
<li>[https://www.jstor.org/stable/90970?origin=ads G. H. Darwin (1908, Philosophical Transactions of the Royal Society A, Vol. 208, pp. 1 - 19)], ''Further Consideration of the Stability of the Pear-Shaped Figure of a Rotating Mass of Liquid.'' &nbsp; <math>\leftarrow</math> &nbsp; Darwin points out that Liapounoff's (1905) work concludes that the "Pear-Shaped" figure is ''unstable,'' whereas in his own 1903 work, Darwin <font color="darkgreen">"&hellip; had arrived at an opposite conclusion."</font>  In this 1908 publication, Darwin has changed his conclusion and is now in agreement with Liapounoff.</li>
<li>[https://ui.adsabs.harvard.edu/abs/1995ApJ...446..500C/abstract D. M. Christodoulou, D. Kazanas, I. Shlosman, and J. E. Tohline (1995, ApJ, Vol. 446, p. 500 - 509)], ''Phase-Transition Theory of Instabilities. &nbsp; III. &nbsp; The Third-Harmonic Bifurcation on the Jacobi Sequence and the Fission Problem.''</li>
</ul>


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