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• 18:47, 12 December 2023 Joel2 talk contribs created page SSC/Structure/BiPolytropes/Analytic1.53 (Created page with "__FORCETOC__ =BiPolytrope with (n_c, n_e) = (3/2, 3)= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:white;" | <font size="-1"><b>Milne</b><br /> (1930)</font> |} Here we lay out the procedure for constructing a bipolytrope in which the core has an...")
• 18:41, 12 December 2023 Joel2 talk contribs created page 2DStructure/AxisymmetricInstabilities (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Axisymmetric Instabilities to Avoid= {| class="AxisymmetricConfigurations" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:white;" |<b>Axisymmetric<br />Instabilities<br />to Avoid</b> |} When constructing rotating equilibrium configurations...")
• 18:31, 12 December 2023 Joel2 talk contribs created page PGE/ConservingMomentum (Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Euler Equation (Conserving Momentum)= ==Various Forms== ===Lagrangian Representation=== Among the principal governing equations we have included the <div align="center"> <span id="ConservingMomentum:Lagrangian"><font color="#770000">'''Lagrangian Representation'''</font></span><br /> of the Euler Equation, {{ Math/EQ_Euler01 }} </div> Multiplying thi...")
• 12:58, 12 December 2023 Joel2 talk contribs created page File:JacobiMaclaurin2.gif
• 12:58, 12 December 2023 Joel2 talk contribs uploaded File:JacobiMaclaurin2.gif
• 12:55, 12 December 2023 Joel2 talk contribs created page File:Dissertation.fig3cropped.png
• 12:55, 12 December 2023 Joel2 talk contribs uploaded File:Dissertation.fig3cropped.png
• 12:53, 12 December 2023 Joel2 talk contribs created page File:Minitorus.animated.gif
• 12:53, 12 December 2023 Joel2 talk contribs uploaded File:Minitorus.animated.gif
• 12:49, 12 December 2023 Joel2 talk contribs created page File:N1.5j2 Combinedsmall.png
• 12:49, 12 December 2023 Joel2 talk contribs uploaded File:N1.5j2 Combinedsmall.png
• 12:45, 12 December 2023 Joel2 talk contribs created page File:TorusMovie1.gif
• 12:45, 12 December 2023 Joel2 talk contribs uploaded File:TorusMovie1.gif
• 12:42, 12 December 2023 Joel2 talk contribs created page File:Apollonian myway4.png
• 12:42, 12 December 2023 Joel2 talk contribs uploaded File:Apollonian myway4.png
• 12:39, 12 December 2023 Joel2 talk contribs created page File:MovieWongN4.gif
• 12:39, 12 December 2023 Joel2 talk contribs uploaded File:MovieWongN4.gif
• 19:14, 11 December 2023 Joel2 talk contribs created page File:OutputC.gif
• 19:14, 11 December 2023 Joel2 talk contribs uploaded File:OutputC.gif
• 19:07, 11 December 2023 Joel2 talk contribs created page File:Schwarzschild1941movie.gif
• 19:07, 11 December 2023 Joel2 talk contribs uploaded File:Schwarzschild1941movie.gif
• 19:05, 11 December 2023 Joel2 talk contribs created page File:TaffVanHorn1974Harmonic.gif
• 19:05, 11 December 2023 Joel2 talk contribs uploaded File:TaffVanHorn1974Harmonic.gif
• 19:05, 11 December 2023 Joel2 talk contribs created page File:TaffVanHorn1974Fundamental.gif
• 19:05, 11 December 2023 Joel2 talk contribs uploaded File:TaffVanHorn1974Fundamental.gif
• 19:03, 11 December 2023 Joel2 talk contribs created page File:Sterne1937SolutionPlot1.png
• 19:03, 11 December 2023 Joel2 talk contribs uploaded File:Sterne1937SolutionPlot1.png
• 19:01, 11 December 2023 Joel2 talk contribs created page File:ImageOfDerivations08GoodRosseland.png
• 19:01, 11 December 2023 Joel2 talk contribs uploaded File:ImageOfDerivations08GoodRosseland.png
• 19:01, 11 December 2023 Joel2 talk contribs created page File:ImageOfDerivations07GoodLedouxWalraven.png
• 19:01, 11 December 2023 Joel2 talk contribs uploaded File:ImageOfDerivations07GoodLedouxWalraven.png
• 19:01, 11 December 2023 Joel2 talk contribs created page File:ImageOfDerivations06GoodJeansBonnor.png
• 19:01, 11 December 2023 Joel2 talk contribs uploaded File:ImageOfDerivations06GoodJeansBonnor.png
• 18:56, 11 December 2023 Joel2 talk contribs created page File:TurningPoints51Bipolytropes.png
• 18:56, 11 December 2023 Joel2 talk contribs uploaded File:TurningPoints51Bipolytropes.png
• 18:52, 11 December 2023 Joel2 talk contribs created page File:MassVsRadiusCombined02.png
• 18:52, 11 December 2023 Joel2 talk contribs uploaded File:MassVsRadiusCombined02.png
• 17:54, 11 December 2023 Joel2 talk contribs created page File:Maclaurin01.gif
• 17:54, 11 December 2023 Joel2 talk contribs uploaded File:Maclaurin01.gif
• 17:50, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ SShydrostaticBalance01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dP}{dr} = - \frac{GM_r \rho}{r^2}</math> </td> </tr> </table>")
• 17:49, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ SSLaneEmden02 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{1}{\xi^2} \frac{d}{d\xi}\biggl( \xi^2 \frac{d\psi}{d\xi} \biggr) = e^{-\psi}</math> </td> </tr> </table>")
• 17:48, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ SSLaneEmden01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{1}{\xi^2} \frac{d}{d\xi}\biggl( \xi^2 \frac{d\Theta_H}{d\xi} \biggr) = - \Theta_H^n</math> </td> </tr> </table>")
• 17:47, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ RadialPulsation03 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math>0 = \frac{d^2x}{d\xi^2} + \biggl[4 - \xi \biggl( \frac{d\psi}{d\xi} \biggr) \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} + \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_\mathrm{g}}\biggr)\xi^2 - \alpha \xi \biggl( \frac{d\psi}{d\xi} \biggr) \biggr] \frac{x}{\xi^2} </math> </td> </tr> <tr> <td alig...")
• 17:46, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ RadialPulsation02 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math>0 = \frac{d^2x}{d\xi^2} + \biggl[ 4 - (n+1) Q \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} + (n+1) \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_g } \biggr) \frac{\xi^2}{\theta} - \alpha Q\biggr] \frac{x}{\xi^2} </math> </td> </tr> <tr> <td align="center" colspan="2"> where:    <math>Q(\x...")
• 17:40, 11 December 2023 Joel2 talk contribs created page Apps/RiemannEllipsoidsCompressible (Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ --> =Compressible Analogs of Riemann S-Type Ellipsoids= Here we attempt to develop a self-consistent-field type, iterative technique that will permit the construction of steady-state structures that are compressible analogs of Riemann S-Type (incompressible) ellipsoids. We will build upon the recent work of [http://adsabs.harvard.edu/abs/2006ApJ...639..549O Ou (2006)]. ==Standard Stea...")
• 17:35, 11 December 2023 Joel2 talk contribs created page PGE/RotatingFrame (Created page with "__FORCETOC__ <!-- __NOTOC__ --> <font color="red"><b> NOTE to Eric Hirschmann & David Neilsen... </b></font> I have moved the earlier contents of this page to a new Wiki location called Compressible Riemann Ellipsoids. =Rotating Reference Frame= At times, it can be useful to view the motion of a fluid from a frame of reference that is rotating with a uniform (''i.e.,'' time-independent) angular velocity <math>~\Omega_f</math>...")
• 17:28, 11 December 2023 Joel2 talk contribs created page AxisymmetricConfigurations/SolutionStrategies (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Axisymmetric Configurations (Solution Strategies)= <!-- Equilibrium, axisymmetric '''structures''' are obtained by searching for time-independent, steady-state solutions to the identified set of simplified governing equations. We begin by writing each governing equation in Eulerian form and setting all partial time-derivatives to zero: <div a...")
• 17:17, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Euler04 (Created page with "<math>\frac{\partial\vec{v}}{\partial t} + \vec\zeta \times \vec{v}= - \frac{1}{\rho} \nabla P - \nabla \biggl[\Phi + \frac{1}{2}v^2 \biggr] </math>")
• 17:15, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Euler03 (Created page with "<math>\frac{\partial(\rho\vec{v})}{\partial t} + \nabla\cdot [(\rho\vec{v})\vec{v}]= - \nabla P - \rho \nabla \Phi</math>")
• 17:13, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Euler02 (Created page with "<math>\frac{\partial\vec{v}}{\partial t} + (\vec{v}\cdot \nabla) \vec{v}= - \frac{1}{\rho} \nabla P - \nabla \Phi</math>")