Editing SSCpt2/SolutionStrategies (section)

===Technique 3===
As in Technique #2, we replace <math>~dP/\rho</math> by <math>~dH</math> in the hydrostatic balance relation, but this time we realize that the resulting expression can be written in the form,

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<math>~\frac{d}{dr}(H+\Phi) = 0 \, .</math>
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This means that, throughout our configuration, the functions {{Math/VAR_Enthalpy01}}<math>(\rho)~</math> and {{Math/VAR_NewtonianPotential01}}<math>(\rho)~</math> must sum to a constant value, call it <math>~C_\mathrm{B}</math>.  That is to say, the statement of hydrostatic balance reduces to the ''algebraic'' expression,

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<math>H + \Phi = C_\mathrm{B} \, .</math>
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This relation must be solved in conjunction with the Poisson equation,

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<math>~\frac{1}{r^2} \frac{d }{dr} \biggl( r^2 \frac{d \Phi}{dr} \biggr)  = 4\pi G \rho \, ,</math>
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giving us two equations (one algebraic and the other a <math>2^\mathrm{nd}</math>-order ODE) that relate the three unknown functions, {{Math/VAR_Enthalpy01}}, {{Math/VAR_Density01}}, and {{Math/VAR_NewtonianPotential01}} to one another.


<b>Self-Consistent Field (SCF) Technique:</b>
* Spherical polytropes &#8212;
** [[SSC/Structure/Polytropes#Tabulated_Properties|Some tabulated global properties]].
** Outline of [[SSC/Structure/Polytropes#HSCF_Technique|our implementation of the HSCF scheme]].