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SSC/Stability/n1PolytropeLAWE/Pt3 - Revision history
2026-04-25T01:31:40Z
Revision history for this page on the wiki
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https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Stability/n1PolytropeLAWE/Pt3&diff=3295&oldid=prev
Joel2: /* Second Attempt */
2026-01-11T18:58:48Z
<p><span class="autocomment">Second Attempt</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:58, 11 January 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l641">Line 641:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Now consider the,</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span id="Consider"></ins>Now consider<ins style="font-weight: bold; text-decoration: none;"></span> </ins>the,</div></td></tr>
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Joel2
https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Stability/n1PolytropeLAWE/Pt3&diff=3294&oldid=prev
Joel2: /* Second Attempt */
2026-01-11T18:41:36Z
<p><span class="autocomment">Second Attempt</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:41, 11 January 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1081">Line 1,081:</td>
<td colspan="2" class="diff-lineno">Line 1,081:</td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Recalling that,</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><span id="</ins>Recalling<ins style="font-weight: bold; text-decoration: none;">">Recalling</span> </ins>that,</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div align="center"></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div align="center"></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>~Q = \biggl[1- \eta\cot(\eta-B) \biggr] \, ,</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>~Q = \biggl[1- \eta\cot(\eta-B) \biggr] \, ,</math></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>~\biggl(\frac{A}{\phi } \biggr)^2 = 1 \, .</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math>~\biggl(\frac{A}{\phi } \biggr)^2 = 1 \, .</math></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Third Attempt===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Third Attempt===</div></td></tr>
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Joel2
https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Stability/n1PolytropeLAWE/Pt3&diff=2953&oldid=prev
Joel2: /* Radial Oscillations of n = 1 Polytropic Spheres (Pt 3) */
2025-07-15T17:53:48Z
<p><span class="autocomment">Radial Oscillations of n = 1 Polytropic Spheres (Pt 3)</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:53, 15 July 2025</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <td align="center" rowspan="1" bgcolor="lightblue" width="<del style="font-weight: bold; text-decoration: none;">33</del>%"><br />[[SSC/Stability/n1PolytropeLAWE|Part I: &nbsp; Search for Analytic Solutions]]<br />&nbsp;</td></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <td align="center" rowspan="1" bgcolor="lightblue" width="<ins style="font-weight: bold; text-decoration: none;">25</ins>%"><br />[[SSC/Stability/n1PolytropeLAWE|Part I: &nbsp; Search for Analytic Solutions]]<br />&nbsp;</td></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <td align="center" rowspan="1" bgcolor="lightblue" width="<del style="font-weight: bold; text-decoration: none;">33</del>%"><br />[[SSC/Stability/n1PolytropeLAWE/Pt2|Part II:&nbsp; New Ideas]]<br />&nbsp;</td></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <td align="center" rowspan="1" bgcolor="lightblue" width="<ins style="font-weight: bold; text-decoration: none;">25</ins>%"><br />[[SSC/Stability/n1PolytropeLAWE/Pt2|Part II:&nbsp; New Ideas]]<br />&nbsp;</td></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <td align="center" rowspan="1" bgcolor="lightblue"><br />[[SSC/Stability/n1PolytropeLAWE/Pt3|III:&nbsp; What About Bipolytropes?]]<br />&nbsp;</td></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> <td align="center" rowspan="1" bgcolor="lightblue<ins style="font-weight: bold; text-decoration: none;">" width="25%</ins>"><br />[[SSC/Stability/n1PolytropeLAWE/Pt3|<ins style="font-weight: bold; text-decoration: none;">Part </ins>III:&nbsp; What About Bipolytropes?<ins style="font-weight: bold; text-decoration: none;">]]<br />&nbsp;</td></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> <td align="center" rowspan="1" bgcolor="lightblue"><br />[[SSC/Stability/n1PolytropeLAWE/Pt4|Part IV:&nbsp; Most General Structural Solution</ins>]]<br />&nbsp;</td></div></td></tr>
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Joel2
https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Stability/n1PolytropeLAWE/Pt3&diff=1355&oldid=prev
Joel2 at 02:05, 21 January 2024
2024-01-21T02:05:41Z
<p></p>
<a href="https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Stability/n1PolytropeLAWE/Pt3&diff=1355&oldid=1354">Show changes</a>
Joel2
https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Stability/n1PolytropeLAWE/Pt3&diff=1354&oldid=prev
Joel2: Created page with "__FORCETOC__ =Radial Oscillations of n = 1 Polytropic Spheres (Pt 3)= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />Part I: Search for Analytic Solutions<br /> </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />Part II: New Ideas<br /> </td> <td align="center" ro..."
2024-01-21T01:53:11Z
<p>Created page with "__FORCETOC__ =Radial Oscillations of n = 1 Polytropic Spheres (Pt 3)= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br /><a href="/JETohline/index.php/SSC/Stability/n1PolytropeLAWE" title="SSC/Stability/n1PolytropeLAWE">Part I: Search for Analytic Solutions</a><br /> </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br /><a href="/JETohline/index.php/SSC/Stability/n1PolytropeLAWE/Pt2" title="SSC/Stability/n1PolytropeLAWE/Pt2">Part II: New Ideas</a><br /> </td> <td align="center" ro..."</p>
<p><b>New page</b></p><div>__FORCETOC__<br />
=Radial Oscillations of n = 1 Polytropic Spheres (Pt 3)=<br />
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<td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />[[SSC/Stability/n1PolytropeLAWE|Part I: &nbsp; Search for Analytic Solutions]]<br />&nbsp;</td><br />
<td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />[[SSC/Stability/n1PolytropeLAWE/Pt2|Part II:&nbsp; New Ideas]]<br />&nbsp;</td><br />
<td align="center" rowspan="1" bgcolor="lightblue"><br />[[SSC/Stability/n1PolytropeLAWE/Pt3|III:&nbsp; What About Bipolytropes?]]<br />&nbsp;</td><br />
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=See Also=<br />
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Joel2