Editing SSC/Stability/n1PolytropeLAWE/Pt3 (section)

====Brute-Force Trial Fit====
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[[File:BruteForceWhiteBoardsmall.png|500px|Photo of white board with steps showing development of trial eigenfunction.  This should be paired with an Excel spreadsheet.]]
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Using a couple of separate Excel spreadsheets &#8212; FaulknerBipolytrope2.xlsx/mu100Mode0 and AnalyticTrialBipolytropeA.xlsx/Sheet2, both stored in a DropBox account under the folder Wiki_edits/Bipolytrope/LinearPerturbation &#8212; we used an inelegant and inefficient trial &amp; error technique in search of an eigenfunction that had the same analytic ''form'' as the one represented above for <math>~x_P</math>, but that, when plotted, appeared to qualitatively match the numerically determined envelope eigenfunction.  Then, on a whiteboard &#8212; see the photo, here on the right &#8212; we formulated a concise expression for a trial function that seemed to work pretty well.  Our primary finding was that <math>~\alpha</math>, appearing as the argument to the <math>~\tan\alpha</math> function, needed to be shifted by something like <math>~-3\pi/4</math>.

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<p>&nbsp;</p><p>THIS SPACE</p><p> INTENTIONALLY</p><p> LEFT BLANK</p>
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