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===Axisymmetric Equilibrium Structures=== {| class="Chap8A" width=100% style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 3px; border-color:darkgrey;" |- ! style="height: 30px; width: 800px; background-color:lightgrey;"|<font color="white" size="+1">2D STRUCTURE</font> |} <p> </p> {| class="Chap8B" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black;" |- ! style="height: 150px; width: 150px; background-color:lightgreen; border-right:2px solid black;" |[[AxisymmetricConfigurations/Equilibria|<b>Constructing<br />Steady-State<br />Axisymmetric<br />Configurations</b>]] | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[2DStructure/AxisymmetricInstabilities|Axisymmetric<br />Instabilities<br />to Avoid]] | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[AxisymmetricConfigurations/SolutionStrategies#Simple_Rotation_Profile_and_Centrifugal_Potential|''Simple''<br />Rotation<br />Profiles]] | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[AxisymmetricConfigurations/HSCF|Hachisu Self-Consistent-Field<br />[HSCF]<br />Technique]] | ! style="height: 150px; width: 150px; " |[[AxisymmetricConfigurations/SolvingPE#Common_Theme:_Determining_the_Gravitational_Potential_for_Axisymmetric_Mass_Distributions|Solving the<br />Poisson Equation]] |} <p> </p> {| class="Chap8C" style="margin-right: auto; margin-left: 230px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; border-right:2px dotted black;" |[[2DStructure/UsingTC#Common_Theme:_Determining_the_Gravitational_Potential_for_Axisymmetric_Mass_Distributions|Using<br />Toroidal Coordinates<br />to Determine the<br />Gravitational<br /> Potential]] | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[File:Apollonian_myway4.png|150px|link=2DStructure/ToroidalCoordinateIntegrationLimits#Mapping_from_Cylindrical_to_Toroidal_Coordinates|Apollonian Circles]] | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[2DStructure/TCsimplification#Common_Theme:_Determining_the_Gravitational_Potential_for_Axisymmetric_Mass_Distributions|Attempt at<br />Simplification<br /><br /><font color="green" size="+2">♥</font>]] | ! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dotted black;" |[[Apps/WongAP#Common_Theme:_Determining_the_Gravitational_Potential_for_Axisymmetric_Mass_Distributions|Wong's<br />Analytic Potential<br />(1973)]] | ! style="height: 150px; width: 150px; background-color:#D0FFFF;" |[[File:MovieWongN4.gif|130px|link=Apps/DysonWongTori#The_Coulomb_Potential|n = 3 contribution to potential]] |} ====Spheroidal & Spheroidal-Like==== <br /> {| class="Chap9A" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |[[Apps/MaclaurinSpheroids#Maclaurin_Spheroids_.28axisymmetric_structure.29|<b>Uniform-Density<br />(Maclaurin)<br />Spheroids</b>]] | ! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dotted black;" |[[Apps/MaclaurinSpheroids/GoogleBooks#Excerpts_from_A_Treatise_of_Fluxions|Maclaurin's<br />Original Text<br />&<br />Analysis<br />(1742)]] | ! style="height: 200px; width: 200px; border-right:2px dashed black;" |[[File:Maclaurin01.gif|282px|link=Apps/MaclaurinSpheroids/GoogleBooks#Prolate_Spheroid|Our Construction of Maclaurin's Figure 291Pt2]] | ! style="height: 150px; width: 150px; border-right:2px solid black; background-color:maroon;" |[[Apps/MaclaurinSpheroidSequence|<font color="white">Maclaurin<br />Spheroid<br />Sequence</font>]] |} <p> </p> {| class="Chap9B" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Rotationally<br />Flattened<br />Isothermal<br />Configurations</b> | ! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dashed black;" |[[Apps/HayashiNaritaMiyama82#Rotationally_Flattened_Isothermal_Structures|Hayashi, Narita<br /> & Miyama's<br />Analytic Sol'n<br />(1982)]] | ! style="height: 150px; width: 150px;" |[[Apps/ReviewStahler83|Review of<br /> Stahler's (1983)<br />Sol'n Technique]] |} <p> </p> {| class="Chap9C" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Rotationally<br />Flattened<br />Polytropes</b> | ! style="height: 150px; width: 150px;" |[[Apps/RotatingPolytropes|Example<br />Equilibria]] |} <p> </p> {| class="Chap9D" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Rotationally<br />Flattened<br />White Dwarfs</b> | ! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dashed black;" |[[Apps/OstrikerBodenheimerLyndenBell66|Ostriker<br />Bodenheimer<br />& Lynden-Bell<br />(1966)]] | ! style="height: 150px; width: 150px;" |[[Apps/RotatingWhiteDwarfs|Example<br />Equilibria]] |} ====Toroidal & Toroidal-Like==== <br /> {| class="Chap10B" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Massless<br />Polytropic<br />Configurations</b> | ! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dotted black;" |[[Apps/PapaloizouPringleTori#Massless_Polytropic_Tori|Papaloizou-Pringle<br />Tori<br />(1984)]] | ! style="height: 150px; width: 250px; background-color:#D0FFFF;" |[[File:TorusMovie1.gif|250px|link=Apps/PapaloizouPringleTori#Boundary_Conditions|Pivoting PP Torus]] |} <p> </p> {| class="Chap10C" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Self-Gravitating<br />Incompressible<br />Configurations</b> | ! style="height: 150px; width: 150px; background-color:#ffeeee; border-right:2px dashed black;" |[[Apps/DysonPotential|Dyson<br />(1893)]] | ! style="height: 150px; width: 150px; border-right:2px dashed black;" |[[Apps/DWT#Common_Theme:_Determining_the_Gravitational_Potential_for_Axisymmetric_Mass_Distributions|Dyson-Wong<br />Tori]] | ! style="height: 150px; width: 150px; " |[[Apps/MaclaurinToroid|Maclaurin<br />Toroid Sequence]]<br />{{ MPT77hereafter }} |} <p> </p> {| class="Chap10D" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99; border-right:2px solid black; " |<b>Self-Gravitating<br />Compressible<br />Configurations</b> | ! style="height: 150px; width: 150px;" |[[Apps/Ostriker64|Ostriker<br />(1964)]] |} <p> </p>
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