Editing SSC/PerspectiveReconciliation (section)

===Lagrangian Approach===
In [[SSC/Perturbations#Spherically_Symmetric_Configurations_.28Stability_.E2.80.94_Part_II.29|another related discussion]], we have shown that, from a standard Lagrangian perspective, the perturbation and linearization of the principal governing equations leads to an equation of continuity (EOC), and equation of motion (EOM) ''already combined'' with the Poisson equation of the form,
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>~d</math>
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>~- 3x - r_0 \biggl(\frac{dx}{dr_0}\biggr) \, ;</math>
  </td>
</tr>

<tr>
  <td align="right">
<math>~\frac{\gamma P_0}{\rho_0} \biggl[ \frac{d}{dr_0}\biggl(d \biggr) \biggr]</math>
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>~\omega^2 r_0 x + g_0\biggl[ 4x + \gamma d \biggr] \, .</math>
  </td>
</tr>
</table>
</div>
The standard <font color="red">''Lagranian''</font> approach to combining these expressions is to <font color="red">take the radial-derivative of the EOC, then substitute the EOC's expression for <math>~d</math> as well as its radial derivative into the EOM</font> to obtain,
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<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>~- \frac{\gamma P_0}{\rho_0} \biggl[ 4\biggl(\frac{dx}{dr_0}\biggr) + r_0 \frac{d^2x}{dr_0^2} \biggr]</math>
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>~\omega^2 r_0 x + g_0\biggl\{ 4x - \gamma \biggl[ 3x + r_0 \biggl(\frac{dx}{dr_0}\biggr) \biggr] \biggr\} \, ,</math>
  </td>
</tr>
</table>
</div>
which, after rearrangement of terms, gives what we have [[SSC/Perturbations#2ndOrderODE|referred to elsewhere as the Adiabatic Wave (or Radial Pulsation) Equation]].