Editing SSC/FreeEnergy/EquilibriumSequenceInstabilities (section)

====Tassoul (1978)====
From pp. 449-450 of [<b>[[User:Tohline/Appendix/References#T78|<font color="red">T78</font>]]</b>] &#8212; ''verbatum'' text in green:  <font color="green">
In Roche's particular problem, the secondary is treated as a rigid sphere; hence, over the primary, the tide-generating potential can be expanded in the form
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<math>~ -\frac{GM^'}{d} \biggl( 1 + \frac{x_1}{d} + \frac{x_1^2 - \tfrac{1}{2}x_2^2 - \tfrac{1}{2}x_3^2}{d^2} + \cdots \biggr) \, .</math>
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<font color="green">The approximation that underlies the theory is to omit all terms beyond those written down.  On this assumption, we find that, apart from its own gravitation, the primary may be supposed to be acted upon by a total field of force derived from the potential
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<math>~-\tfrac{1}{2}\Omega^2(x_1^2 + x_x^2) - \mu(x_1^2 - \tfrac{1}{2}x_2^2 - \tfrac{1}{2}x_3^2) - \biggl(\mu - \frac{M^'}{M+M^'} \Omega^2\biggr) dx_1 \, ,</math>
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<font color="green">where</font>
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<math>~\mu</math>
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<math>~=</math>
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<math>~\frac{GM^'}{d^3} \, .</math>
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<font color="green">Further letting <math>~\Omega^2</math> have its "Keplerian value"</font>
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<math>~\Omega^2</math>
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<math>~=</math>
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<math>~\frac{G(M+M^')}{d^3} \, ,</math>
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<font color="green">we can thus write the conditions of relative equilibrium for the primary in the form</font>
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<math>~\frac{1}{\rho} \nabla p</math>
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<math>~=</math>
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<math>~
-\nabla [ V
-\tfrac{1}{2}\Omega^2(x_1^2 + x_x^2) - \mu(x_1^2 - \tfrac{1}{2}x_2^2 - \tfrac{1}{2}x_3^2) ] \, ,
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<font color="green">where <math>~V</math> is the self-gravitating potential of the primary.</font>