Editing SSC/PerspectiveReconciliation (section)

===Eulerian Approach===
In a [[SSC/StabilityEulerianPerspective#Stability_of_Spherically_Symmetric_Configurations_.28Eulerian_Perspective.29|related discussion]], we have shown that, from a standard Eulerian perspective, the perturbation and linearization of the [[PGE#Principal_Governing_Equations|principal governing equations]] leads to an equation of continuity (EOC), equation of motion (EOM), and Poisson equation of the form,
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<math>~- \nabla\cdot \vec{v}</math>
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<math>~=</math>
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<math>~
\frac{\partial}{\partial t}\biggl( \frac{\rho_1}{\rho_0} \biggr) + \vec{v} \cdot \frac{\nabla\rho_0}{\rho_0} \, ;
</math>
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<math>~\frac{\partial \vec{v}}{\partial t}</math>
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<math>~=</math>
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<math>~
- \nabla\Phi_1 - \nabla\biggl[ \frac{\rho_1}{\rho_0}\biggl( \frac{dP}{d\rho} \biggr)_0 \biggr] \, ;
</math>
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<math>~\nabla^2\Phi_1</math>
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<math>~=</math>
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<math>~
4\pi G \rho_1 \, .
</math>
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The standard <font color="red">''Eulerian''</font> approach to combining these expressions is to <font color="red">take the time-derivative of the EOC, take the divergence of the EOM (and combine with the Poisson equation), then add the two</font> to obtain,
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<math>~
\frac{\partial^2}{\partial t^2}\biggl( \frac{\rho_1}{\rho_0} \biggr) + \frac{\nabla\rho_0}{\rho_0} \cdot \frac{\partial \vec{v}}{\partial t} 
- 4\pi G \rho_1 - \nabla^2 \biggl[ \frac{\rho_1}{\rho_0}\biggl( \frac{dP}{d\rho} \biggr)_0 \biggr] 
</math>
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<math>~=</math>
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<math>~0 \, .
</math>
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After defining the ''fractional Eulerian density variation'' as,
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<math>~s \equiv \frac{\rho_1}{\rho_0} \, ,</math>
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this becomes what we have [[SSC/StabilityEulerianPerspective#EulerianWaveEquation|referred to elsewhere as the Eulerian Wave Equation]].