SSC/Stability/BiPolytropes/RedGiantToPN/Pt2 - Revision history

Joel2: /* Fourth Try */

2026-01-12T21:56:05Z

Fourth Try

← Older revision		Revision as of 17:56, 12 January 2026
Line 1,765:		Line 1,765:

	====Fourth Try====		====Fourth Try====
	Try adding an additional term that was discussed above under "~~Second~~ Try", namely,		Try adding an additional term that was discussed above under "First Try", namely,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

2026-01-12T21:54:47Z

Fourth Try

@@ Line 1,765: / Line 1,765: @@
 ====Fourth Try====
-Try adding an additional term of the form,
+Try adding an additional term that was discussed above under "Second Try", namely,
 <table border="0" cellpadding="5" align="center">
@@ Line 1,798: / Line 1,798: @@
    <td align="left">
 <math>
--\frac{2d}{\eta^3} \, .
+-\frac{2d}{\eta^3} \, ,
 </math>
    </td>

2026-01-12T21:47:10Z

Third Try

@@ Line 1,759: / Line 1,759: @@
 <math>
 \frac{2(b-c)}{\eta^3}\biggl[\cot(B-\eta)  \biggr]
 </math>
    </td>

2026-01-12T21:24:40Z

Third Try

@@ Line 1,745: / Line 1,745: @@
 (1 - Q )\cdot \biggl[\eta \cdot \sin(B-\eta) \biggr]
 \biggr\}
 </math>
    </td>

2026-01-12T19:23:27Z

Third Try

@@ Line 1,711: / Line 1,711: @@
    <td align="left">
 <math>
 \frac{2c}{\eta^3}\biggl[\sin(B-\eta)\biggr]^{-3}\biggl\{
 \eta^2\cdot \cos(B-\eta)

2026-01-12T19:14:12Z

Third Try

← Older revision		Revision as of 15:14, 12 January 2026
Line 1,712:		Line 1,712:
	<math>		<math>
	\frac{2c}{\eta^3}\biggl[\sin(B-\eta)\biggr]^{-3}\biggl\{		\frac{2c}{\eta^3}\biggl[\sin(B-\eta)\biggr]^{-3}\biggl\{
	~~\sin^2(B-\eta)\cos(B-\eta)~~
	~~-\eta\cdot \biggl[\sin(B-\eta)\biggr]~~
	+
	\eta^2\cdot \cos(B-\eta)		\eta^2\cdot \cos(B-\eta)
	~~</math>~~		- \biggl[\sin^2(B-\eta)\cos(B-\eta)\biggr]
	~~</td>~~
	~~</tr>~~

	~~<tr>~~
	~~<td align="right">~~
	~~ ~~
	~~</td>~~
	~~<td align="center">~~
	~~ ~~
	~~</td>~~
	~~<td align="left">~~
	~~<math>~~
	+		+
	(2 -Q )\cdot \biggl[ \eta \cdot \sin(B-\eta) ~~~-~\sin^2(B-\eta)\cos(B-\eta)~~		(1 - Q )\cdot \biggl[\eta \cdot \sin(B-\eta) \biggr]
	\biggr]
	~~~-~ Q \biggl[\sin(B-\eta)\biggr]^{2} \cos(B-\eta)~~
	\biggr\}		\biggr\}
	</math>		</math>

2026-01-12T19:01:01Z

Third Try

@@ Line 1,658: / Line 1,658: @@
    <td align="left">
 <math>
-+ \biggl\{ 4 -2Q \biggr\}\frac{1}{\eta} \cdot \frac{dx_2}{d\eta}
++ \biggl\{ 4 -2Q \biggr\}\cdot \frac{c}{\eta^3}\biggl\{\eta ~-~\sin(B-\eta)\cos(B-\eta)
-~-~  \biggl[ 2 Q \biggr]   \frac{x_2}{\eta^2}
+\biggr\}\biggl[\sin(B-\eta)\biggr]^{-2}
 </math>
    </td>

2026-01-12T18:26:51Z

Third Try

@@ Line 1,559: / Line 1,559: @@
 + \frac{2c}{\eta}\cdot \biggl[\sin(B-\eta)\biggr]^{-3}\cos(B-\eta)
 \biggr\}
 </math>
    </td>

2026-01-12T18:07:00Z

Third Try

← Older revision		Revision as of 14:07, 12 January 2026
Line 1,552:		Line 1,552:
	\biggl\{		\biggl\{
	\frac{2c}{\eta^3}\cdot \cot(B-\eta)		\frac{2c}{\eta^3}\cdot \cot(B-\eta)
	-\frac{c}{\eta^2}\cdot \~~cot~~(B-\eta)		-\frac{c}{\eta^2}\cdot \biggl[\sin(B-\eta)\biggr]^{-2}
	\biggr\}		\biggr\}
	+		+
	\frac{d}{d\eta}\biggl\{		\biggl\{
	\frac{c}{\eta}\cdot \biggl[\sin(B-\eta)\biggr]^{-2}		-\frac{c}{\eta^2}\cdot \biggl[\sin(B-\eta)\biggr]^{-2}
			+ \frac{2c}{\eta}\cdot \biggl[\sin(B-\eta)\biggr]^{-3}\cos(B-\eta)
	\biggr\}		\biggr\}
	</math>		</math>

2026-01-12T17:57:36Z

Third Try

@@ Line 1,386: / Line 1,386: @@
 One at a time:
 <table border="0" cellpadding="5" align="center">
@@ Line 1,514: / Line 1,516: @@
 \frac{c}{\eta^2}\biggl\{\eta ~-~\sin(B-\eta)\cos(B-\eta)
 \biggr\}\biggl[\sin(B-\eta)\biggr]^{-2}
 </math>
    </td>