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• 13:10, 22 June 2024 Joel2 talk contribs created page File:Vol2Paragraph641.png
• 13:10, 22 June 2024 Joel2 talk contribs uploaded File:Vol2Paragraph641.png
• 13:10, 22 June 2024 Joel2 talk contribs created page File:EarthAsOblateSpheroidQuoteSect492.png
• 13:10, 22 June 2024 Joel2 talk contribs uploaded File:EarthAsOblateSpheroidQuoteSect492.png
• 13:09, 22 June 2024 Joel2 talk contribs created page File:ProlateSpheroidQuoteSect491.png
• 13:09, 22 June 2024 Joel2 talk contribs uploaded File:ProlateSpheroidQuoteSect491.png
• 13:08, 22 June 2024 Joel2 talk contribs created page File:MoonOrbitQuoteSect487.png
• 13:08, 22 June 2024 Joel2 talk contribs uploaded File:MoonOrbitQuoteSect487.png
• 13:07, 22 June 2024 Joel2 talk contribs created page File:PlateXXXII vol2.png
• 13:07, 22 June 2024 Joel2 talk contribs uploaded File:PlateXXXII vol2.png
• 13:06, 22 June 2024 Joel2 talk contribs created page File:PlateXXXIII vol2.png
• 13:06, 22 June 2024 Joel2 talk contribs uploaded File:PlateXXXIII vol2.png
• 13:05, 22 June 2024 Joel2 talk contribs created page File:TitlePage2ndEdition01.png
• 13:05, 22 June 2024 Joel2 talk contribs uploaded File:TitlePage2ndEdition01.png
• 13:05, 22 June 2024 Joel2 talk contribs created page File:TitlePage1stEdition01.png
• 13:05, 22 June 2024 Joel2 talk contribs uploaded File:TitlePage1stEdition01.png
• 13:03, 22 June 2024 Joel2 talk contribs created page Apps/MaclaurinSpheroids/GoogleBooks (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Excerpts from A Treatise of Fluxions= {| class="MaclaurinSpheroids" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffeeee;" |<b>Maclaurin's<br />Original Text<br />&<br />Analysis<br />(1742)</b> |} Both Volume I and Volume II of Colin Maclaurin's "''A Tr...")
• 12:59, 22 June 2024 Joel2 talk contribs created page File:MacAtJacBifurcationJustGravity01.png
• 12:59, 22 June 2024 Joel2 talk contribs uploaded File:MacAtJacBifurcationJustGravity01.png
• 12:42, 22 June 2024 Joel2 talk contribs created page Apps/MaclaurinSpheroids (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Maclaurin Spheroids= {| class="MaclaurinSpheroids" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" |<b>Uniform-Density<br />Maclaurin<br />Spheroids</b> |} There is no particular reason why one should guess ahead of time that the equilibrium properti...")
• 12:39, 22 June 2024 Joel2 talk contribs created page Apps/WongAP (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions= You have arrived at this page from our ''Tiled Menu'' by clicking on the chapter title that is also identified, below, by the light-blue-colored icon. You may proceed directly to that chapter by clicking (again) on that highlighted chapter icon. However, we have brought y...")
• 12:36, 22 June 2024 Joel2 talk contribs created page 2DStructure/TCsimplification (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions= You have arrived at this page from our ''Tiled Menu'' by clicking on the chapter title that is also identified, below, by the light-blue-colored icon. You may proceed directly to that chapter by clicking (again) on that highlighted chapter icon. However, we have brought y...")
• 12:33, 22 June 2024 Joel2 talk contribs created page 2DStructure/UsingTC (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions= You have arrived at this page from our ''Tiled Menu'' by clicking on the chapter title that is also identified, below, by the light-blue-colored icon. You may proceed directly to that chapter by clicking (again) on that highlighted chapter icon. However, we have brought y...")
• 19:38, 21 June 2024 Joel2 talk contribs created page File:MovieWongN4b.gif
• 19:38, 21 June 2024 Joel2 talk contribs uploaded File:MovieWongN4b.gif
• 19:37, 21 June 2024 Joel2 talk contribs created page File:Montage04.png
• 19:37, 21 June 2024 Joel2 talk contribs uploaded File:Montage04.png
• 19:36, 21 June 2024 Joel2 talk contribs created page File:MovieWongN2.gif
• 19:36, 21 June 2024 Joel2 talk contribs uploaded File:MovieWongN2.gif
• 19:35, 21 June 2024 Joel2 talk contribs created page File:Wong73OurFig6b.png
• 19:35, 21 June 2024 Joel2 talk contribs uploaded File:Wong73OurFig6b.png
• 19:33, 21 June 2024 Joel2 talk contribs created page File:Wong111N4.png
• 19:33, 21 June 2024 Joel2 talk contribs uploaded File:Wong111N4.png
• 19:26, 21 June 2024 Joel2 talk contribs created page Apps/Wong1973Potential (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Wong's (1973) Analytic Potential= ==Technical Background Review== Drawing principally from the published works of {{ Wong73full }} and {{ CT99full }}, in an accompanying discussion we have detailed how the gravitational potential of any finite mass distribution can be determined using toroidal coordinates, rathe...")
• 19:24, 21 June 2024 Joel2 talk contribs created page File:Wong73VaryingRoverd.gif
• 19:24, 21 June 2024 Joel2 talk contribs uploaded File:Wong73VaryingRoverd.gif
• 19:23, 21 June 2024 Joel2 talk contribs created page File:MovieWongComposite.gif
• 19:23, 21 June 2024 Joel2 talk contribs uploaded File:MovieWongComposite.gif
• 19:20, 21 June 2024 Joel2 talk contribs created page File:FlatColorContoursCropped.png
• 19:20, 21 June 2024 Joel2 talk contribs uploaded File:FlatColorContoursCropped.png
• 19:09, 21 June 2024 Joel2 talk contribs created page 2DStructure/ToroidalGreenFunction (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Using Toroidal Coordinates to Determine the Gravitational Potential= NOTE:   An earlier version of this chapter has been shifted to our "Ramblings" Appendix. Here we build upon our accompanying review of...")
• 19:05, 21 June 2024 Joel2 talk contribs created page 2DStructure/ToroidalCoordinates (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Using Toroidal Coordinates to Determine the Gravitational Potential= ==Preface== <table border="1" width="90%" align="center" cellpadding="15"> <tr><td align="left"> <table border="0" cellpadding="8" align="center" width="60%"> <tr><td align="center"> <font size="+1"><b>Abstract</b></font><br />Joel E. Tohline (September, 2017) </td></tr> </table> <table border="0" cellpadding="3" align="center" width="60%"> <tr><td...")
• 18:57, 21 June 2024 Joel2 talk contribs created page AxisymmetricConfigurations/PoissonEq (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Solving the (Multi-dimensional) Poisson Equation Numerically= ==Overview== The set of Principal Governing Equations that serves as the foundation of our study of the structure, stability, and dynamical evolution of self-gravitating fluids contains an equation of motion (the ''Euler'' equation) that includes an acceleration due to local gradients in the (Newtonian) gravitational p...")
• 18:54, 21 June 2024 Joel2 talk contribs created page Apps/DysonWongTori (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Self-Gravitating, Incompressible (Dyson-Wong) Tori= <!--Much of the introductory material of this chapter has been drawn from the paper by [http://adsabs.harvard.edu/abs/1990ApJ...361..394T Tohline & Hachisu (1990)] titled, ''The Breakup of Self-Gravitating Rings, Tori, and Accretion Disks.''--> <table border="1" cellpadding="8" align="center"> <tr> <th algin="center" colspan="5"> Schematics Illustrating ''Anch...")
• 18:49, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme3B (Created page with "Beginning with ''his'' integral expression for <math>\Phi(\eta,\theta)|_\mathrm{axisym}</math>, {{ Wong73 }} was able to complete the integrals in ''both'' coordinate directions and obtain an analytic expression for the potential both inside and outside of a uniformly charged (equivalently, uniform-density), circular torus. <font color="orange">This is a remarkable result that has been largely unnoticed and unappreciated by the astrophysics community.</font> We detail...")
• 18:48, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme3A (Created page with "Referencing [<b><font color="red">MF53</font></b>], {{ Wong73full }} developed an integral expression for the Coulomb (equivalently, gravitational) potential whose foundation is the single summation, Green's function expression for the reciprocal distance between two points in toroidal coordinates. For axisymmetric mass distributions^‡, Wong obtained, <table border="0" cellpadding="5" align="center"> <tr> <td align="righ...")
• 18:47, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme3 (Created page with "Now, beginning with Version 2 of our expression for the ''Gravitational Potential of Axisymmetric Mass Distributions'', let's also map the (unprimed) cylindrical coordinate pair, <math>~(\varpi, z)</math>, to the same (but, unprimed) toroidal coordinate system, <math>~(\eta,\theta)</math>, and place the toroidal coordinate system's ''anchor ring'' in the equatorial plane of the cylindrical-coordinate system such that, <math>~(\varpi_a,z_a) = (a,0)</math>. This gives, wh...")
• 18:46, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme2A (Created page with "Referencing (equivalently, Version 1 of) the above-identified integral expression for the ''Gravitational Potential of an Axisymmetric Mass Distribution,'' [http://adsabs.harvard.edu/abs/2012MNRAS.424.2635T Trova, Huré & Hersant (2012)] offer the following assessment in §6 of their paper: <table border="0" cellpadding="3" align="center" width="60%"> <tr><td align="left"> <font color="darkgreen"> "The important question we have tried to clarify...")
• 18:45, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme2 (Created page with "Suppose we rewrite (Version 1 of) the above-highlighted Key integral expression such that the (primed) coordinate location of each mass element is mapped from cylindrical coordinates <math>~(\varpi^', z^')</math> to a toroidal-coordinate system <math>~(\eta^',\theta^')</math> whose ''anchor ring'' cuts through the meridional plane at the cylindrical-coordinate location, <math>~(\varpi_a,z_a)</math>. This desired mapping is handled via the pair of relations,...")
• 18:44, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme1B (Created page with "[http://adsabs.harvard.edu/abs/1974ApJ...194..393D Deupree (1974)] and, separately, [http://adsabs.harvard.edu/abs/1983ApJ...268..155S Stahler (1983a)] have argued that a reasonably good approximation to the gravitational potential due to any extended axisymmetric mass distribution can be obtained by adding up the contributions due to many ''thin rings'' — with <math>~\delta M(\varpi^', z^')</math> being the appropriate differential mass contributed by each ring e...")