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23:06, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893Part2hereafter (Created page with "Dyson1893Part2")
23:05, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893Part2full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1893RSPTA.184.1041D/abstract F. W. Dyson (1893, Phil. Trans. Royal Soc. London. A., Vol. 184, pp. 1041 - 1106)]")
23:04, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893Part2figure (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1893RSPTA.184.1041D/abstract F. W. Dyson (1893)]<br />''The Potential of an Anchor Ring. Part II''<br />Philosophical Transactions of the Royal Society of London. A., Vol. 184, pp. 1041 - 1106")
23:03, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893Part2 (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1893RSPTA.184.1041D/abstract Dyson (1893b)]")
23:01, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893hereafter (Created page with "Dyson1893Part1")
23:01, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893full (Created page with "📚 [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893, Phil. Trans. Royal Soc. London. A., Vol. 184, pp. 43 - 95)]")
23:00, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893figure (Created page with "[http://adsabs.harvard.edu/abs/1893RSPTA.184...43D F. W. Dyson (1893)]<br /> ''The Potential of an Anchor Ring''<br />Philosophical Transactions of the Royal Society of London. A., Vol. 184, pp. 43 - 95")
22:59, 13 December 2023 Joel2 talk contribs created page Template:Dyson1893 (Created page with "📚 [http://adsabs.harvard.edu/abs/1893RSPTA.184...43D Dyson (1893a)]")
22:57, 13 December 2023 Joel2 talk contribs created page Template:Ferrers1877hereafter (Created page with "Ferrers1877")
22:56, 13 December 2023 Joel2 talk contribs created page Template:Ferrers1877full (Created page with "📚 [https://babel.hathitrust.org/cgi/pt?id=uc1.$b417536&view=1up&seq=15 N. M. Ferrers (1877, Quart. J. Pure Appl. Math., Vol. 14, pp. 1 - 22)]")
22:55, 13 December 2023 Joel2 talk contribs created page Template:Ferrers1877figure (Created page with "[https://babel.hathitrust.org/cgi/pt?id=uc1.$b417536&view=1up&seq=15 N. M. Ferrers (1877)]<br />''On the Potentials of Ellipsoids, Ellipsoidal Shells, Elliptic Laminæ, and Elliptic Rings, of Variable Densities''<br />The Quarterly Journal of Pure and Applied Mathematics, Vol. 14, pp. 1 - 22")
22:54, 13 December 2023 Joel2 talk contribs created page Template:Ferrers1877 (Created page with "📚 [https://babel.hathitrust.org/cgi/pt?id=uc1.$b417536&view=1up&seq=15 Ferrers (1877)]")
22:52, 13 December 2023 Joel2 talk contribs created page Template:Lane1870hereafter (Created page with "Lane1870")
22:52, 13 December 2023 Joel2 talk contribs created page Template:Lane1870full (Created page with "📚 [https://archive.org/details/mobot31753002152772/page/56 J. H. Lane (1870, The American Journal of Science and Arts, Vol. 50, pp. 57 - 74)]")
22:51, 13 December 2023 Joel2 talk contribs created page Template:Lane1870figure (Created page with "[https://archive.org/details/mobot31753002152772/page/56 J. H. Lane (1870)]<br />''On the Theoretical Temperature of the Sun<br /> under the Hypothesis of a Gaseous Mass Maintaining Its Volume<br /> by Its Internal Heat and Depending on the Laws of Gases Known to Terrestrial Experiment''<br />The American Journal of Science and Arts, Vol. 50, pp. 57 - 74")
22:50, 13 December 2023 Joel2 talk contribs created page Template:Lane1870 (Created page with "📚 [https://archive.org/details/mobot31753002152772/page/56 Lane (1870)]")
22:47, 13 December 2023 Joel2 talk contribs created page Template:Clausius1870full (Created page with "📚 [https://www.tandfonline.com/doi/abs/10.1080/14786447008640370 R. J. E. Clausius (1870, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Ser. 4, Vol. 40, issue 265, pp. 122 - 127)]")
22:46, 13 December 2023 Joel2 talk contribs created page Template:Clausius1870figure (Created page with "[https://www.tandfonline.com/doi/abs/10.1080/14786447008640370 R. J. E. Clausius (1870)]<br />''On a Mechanical Theorem Applicable to Heat''<br />The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Ser. 4, Vol. 40, issue 265, pp. 122 - 127")
22:46, 13 December 2023 Joel2 talk contribs created page Template:Clausius1870 (Created page with "📚 [https://www.tandfonline.com/doi/abs/10.1080/14786447008640370 Clausius (1870)]")
20:42, 12 December 2023 Joel2 talk contribs created page Template:TT1867hereafter (Created page with "TT1867")
20:41, 12 December 2023 Joel2 talk contribs created page Template:TT1867full (Created page with "📚 [https://books.google.com/books?id=wwO9X3RPt5kC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false W. Thomson & P. G. Tait (1867) Treatise on Natural Philosophy, Oxford at the Clarendon Press (London: MacMillan and Co.)]")
20:40, 12 December 2023 Joel2 talk contribs created page Template:TT1867figure (Created page with "[https://books.google.com/books?id=wwO9X3RPt5kC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false W. Thomson & P. G. Tait (1867)]<br />''Treatise on Natural Philosophy''<br />Oxford at the Clarendon Press (London: MacMillan and Co.)")
20:39, 12 December 2023 Joel2 talk contribs created page Template:TT1867 (Created page with "📚 [https://books.google.com/books?id=wwO9X3RPt5kC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Thomson & Tait (1867)]")
20:36, 12 December 2023 Joel2 talk contribs created page Appendix/References (Created page with "__FORCETOC__  =Journal Articles= ==Explanation== Three or four templates are available for each individual journal-article reference. For example, for the Dyson (1893) publication or for BAC84: <ol type="1"> <li>Dyson1893</li> <li>Dyson1893full</li> <li>Dyson1893figure <math>\Leftarrow</math> This template is highlighted below.</li> <li>BAC84hereafter</li> </ol> If you want to see which of our M...")
20:28, 12 December 2023 Joel2 talk contribs created page Apps/Korycansky Papaloizou 1996 (Created page with "__FORCETOC__  =Korycansky and Papaloizou (1996)= {| class="NonaxisymmetricDisks" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:lightgreen;" |<b>Constructing<br />Infinitesimally Thin<br />Nonaxisymmetric<br />Disks</b> |} [http://adsabs.harvard.edu/abs/1996ApJS..105..181K K...")
19:59, 12 December 2023 Joel2 talk contribs created page File:RmodeImage8.png
19:59, 12 December 2023 Joel2 talk contribs uploaded File:RmodeImage8.png
19:11, 12 December 2023 Joel2 talk contribs created page SSC/Structure/Polytropes (Created page with "__FORCETOC__  =Polytropic Spheres= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | <font size="-1"><b>Isolated<br />Polytropes</b></font> |}  Here we will supplement the SSCpt1/PGE|simplified set of...")
19:06, 12 December 2023 Joel2 talk contribs created page File:Work-in-progress.png
19:06, 12 December 2023 Joel2 talk contribs uploaded File:Work-in-progress.png
19:02, 12 December 2023 Joel2 talk contribs created page Template:SGFworkInProgress (Created page with "---- <div align="center"> 100px|center Material that appears after this point in our presentation is under development and therefore <br />may contain incorrect mathematical equations and/or physical misinterpretations. <br /><font size="-1">| Go Home | </font> </div> ----")
18:58, 12 December 2023 Joel2 talk contribs created page SSC/Structure/BiPolytropes (Created page with "__FORCETOC__ =BiPolytropes= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | <font size="-1"><b>Composite<br />Polytropes</b><br />(Bipolytropes)</font> |} ==Background== While polytropic spheres can give us useful ''general'' insight into the internal s...")
18:54, 12 December 2023 Joel2 talk contribs created page SSC/Perturbations (Created page with "__FORCETOC__   =Spherically Symmetric Configurations (Stability — Part II)=  {| 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">H_BookTiledMenu#Stability_Analysis|<b...")
18:47, 12 December 2023 Joel2 talk contribs created page SSC/Structure/BiPolytropes/Analytic1.53 (Created page with "__FORCETOC__ =BiPolytrope with (n<sub>c</sub>, n<sub>e</sub>) = (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__  =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__   =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...")
15:29, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ TRApproximation (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Other_Equations_with_Assigned_Templates </td> <td align="right"> <math>\Phi_\mathrm{TR}(\varpi,z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math>-\biggl[ \frac{2GM}{\pi } \biggr]\frac{K(k)}{\sqrt{(\varpi+a)^2 + z^2}}</math> </td> </tr> <tr> <td align="center" colspan="4"> <math>\mathrm{where:}~~~k...")
15:27, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ Polytrope03 (Created page with "<math>\rho = \biggl[ \frac{H}{(n+1)K_\mathrm{n}} \biggr]^n </math>")
15:26, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ Polytrope02 (Created page with "<math>H = (n+1)K_\mathrm{n} \rho^{1/n}</math>")
15:25, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ Polytrope01 (Created page with "<math>P = K_\mathrm{n} \rho^{1+1/n}</math>")
15:24, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ EOSideal02 (Created page with "<math>P = (\gamma_\mathrm{g} - 1)\epsilon \rho </math>")
15:23, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ EOSideal00 (Created page with "<math>P = n_g k T</math>")
15:22, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ CT99Axisymmetric (Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Other_Equations_with_Assigned_Templates </td> <td align="right"> <math>\Phi(\varpi,z)\biggr|_\mathrm{axisym}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> - \frac{G}{\pi} \iint\limits_\mathrm{config} \biggl[ \frac{\mu}{(\varpi~ \varpi^')^{1 / 2}} \biggr] K(\mu) \rho(\varpi^', z^') 2\pi \varpi^'~ d\v...")
15:19, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ RadialPulsation04 (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}{dr_0^2} + \frac{1}{r_0}\biggl[4 + \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{dx}{dr_0} + \biggl[ \biggl(3 - \frac{4}{\gamma_g}\biggr) \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{x}{r_0^2} - \frac{1}{\Delta} \biggl[\frac{d\ln P_0}{d\ln r_0}\cdot \frac{\rho_c}{\rho_0} \biggl( \frac{\sigma_c...")
15:18, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ RadialPulsation01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math> \frac{d^2x}{dr_0^2} + \biggl[\frac{4}{r_0} - \biggl(\frac{g_0 \rho_0}{P_0}\biggr) \biggr] \frac{dx}{dr_0} + \biggl(\frac{\rho_0}{\gamma_\mathrm{g} P_0} \biggr)\biggl[\omega^2 + (4 - 3\gamma_\mathrm{g})\frac{g_0}{r_0} \biggr] x = 0 </math> </td> </tr> </table>")
14:48, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ SSradiationTransport01 (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{dT}{dr} = - \frac{ 3 }{ 4a_\mathrm{rad} c} \biggl(\frac{ \kappa \rho }{ T^3 }\biggr) \frac{ L_r }{ 4\pi r^2 }</math> </td> </tr> </table>")
14:47, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ SSmassConservation01 (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{dM_r}{dr} = 4\pi r^2 \rho</math> </td> </tr> </table>")
14:46, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ SSenergyConservation01 (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{dL_r}{dr} = 4\pi r^2 \rho \epsilon_\mathrm{nuc}</math> </td> </tr> </table>")
14:44, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ ZTFG01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right" width="35%"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="left"> <font><math>P_\mathrm{deg} = A_\mathrm{F} F(\chi) </math></font> </td> </tr> <tr> <td align="center" colspan="2"> where: <math>F(\chi) \equiv \chi(2\chi^2 - 3)(\chi^2 + 1)^{1/2} + 3\sinh^{-1}\chi</math> </td> </tr> <tr> <td align="right" colspan="1"> and: </td> <td align="left"...")
14:43, 12 December 2023 Xxsrm talk contribs created page Template:Math/EQ PressureTotal01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="center"> <math>p_\mathrm{total} = \biggl(\frac{\mu_e m_p}{\bar{\mu} m_u} \biggr) 8 \chi^3 \frac{T}{T_e} + F(\chi) + \frac{8\pi^4}{15} \biggl( \frac{T}{T_e} \biggr)^4</math> </td> </tr> </table>")

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