2023-12-17T23:15:26Z

174.64.2.60: /* Equilibrium Structures */

=Primary (Tiled Menu) Chapters=
NOTE:   &clubs; means templates and references to other chapters have been checked for completeness.

==Context==
<ol type="I">
<li>&clubs; [[PGE|Principal Governing Equations]] (PGEs)
<ol type="A">
<li>&clubs; [[Cylindrical3D|Equations Cast in Cylindrical Coordinates]]</li>
</ol>
</li>
<li>&clubs; [[PGE/ConservingMass|Continuity]]</li>
<li>&clubs; [[PGE/Euler|Euler]]
<ol type="A">
<li>[[AxisymmetricConfigurations/SolutionStrategies|Axisymmetric Configurations (Solution Strategies)]]; Double check vector identities   ⇐   also includes "Simple Rotation Profiles"</li>
<li>
&clubs; [[PGE/RotatingFrame|Rotating Reference Frame]]; Euler equation viewed from a rotating frame of reference
<ol type="1">
<li>[[Apps/RiemannEllipsoidsCompressible|Compressible Analogs of Riemann S-Type Ellipsoids]]; Nonlinear velocity cross-product </li>
<li>&clubs; [[Apps/Korycansky_Papaloizou_1996|Korycansky and Papaloizou (1996)]]; Nonlinear velocity cross-product   ⇐   bottom displays [https://digitalcommons.lsu.edu/gradschool_disstheses/6650/ Andalib] velocity maps</li>
</ol>
</li>
<li>&clubs; [[PGE/ConservingMomentum|Euler Equation (Conserving Momentum)]]; Earlier draft of "Euler" presentation</li>
</ol>
</li>
<li>&clubs; [[PGE/FirstLawOfThermodynamics|1st Law of Thermodynamics]]
<ol type="A">
<li>[[Appendix/Ramblings/Radiation/RadHydro|Radiation-Hydrodynamcis]]; Nonadiabatic (optically thick) environments
</li>
</ol>
</li>
<li>&clubs; [[PGE/PoissonOrigin|Poisson]]</li>

<li>&clubs; [[VE|Global Energy Considerations]]</li>

<li>&clubs; [[SR|Equation of State]] (EOS)
<ol type="A">
<li>[[2DStructure/AxisymmetricInstabilities|Axisymmetric Instabilities to Avoid]]; Poincaré-Wavre theorem</li>
<li>[[SSC/Structure/BiPolytropes/Analytic1.53|BiPolytrope with <math>(n_c, n_e) = (\tfrac{3}{2}, 3)</math>]]; The parameter, β</li>
</ol>
</li>

<li>&clubs; [[SR/IdealGas|Ideal Gas]]</li>
<li>&clubs; [[SR/PressureCombinations|Total Pressure]]
<ol type="A">
<li>&clubs; [[SR/Ptot_QuarticSolution|Determining Temperature from Density & Pressure]]; A solution to quartic equation
</li>
</ol>
</li>

<li>&clubs; [[Apps/SMS|Bond, Arnett, & Carr (1984)]]
<ol type="A">
<li>[[SSC/Perturbations|Spherically Symmetric Configurations (Stability — Part II)]]; Brief summary of Ledoux and Pekeris (1941)
</li>
</ol>
</li>
</ol>

==Spherically Symmetric Configurations==
<ol type="I">
<li>&clubs; [[SSCpt1/PGE|One-Dimensional PGEs]]
</li>
<li>[[SSC/Index|SSC Index]]</li>
<li>[[SphericallySymmetricConfigurations/IndexFreeEnergy|Index to Free-Energy and Virial Analyses]]</li>
<li>[[SSCpt1/Virial/PolytropesEmbeddedOutline|Virial Equilibrium of Embedded Polytropic Spheres]]   ⇐   Image of free-energy surface</li>
<li>[[SSCpt1/Virial/FormFactors|Structural Form Factors]]</li>
<li>[[SSCpt1/Virial|Free-Energy of Spherical Systems]]</li>
</ol>

===Equilibrium Structures===
<ol type="I">
<li>[[SSCpt2/IntroductorySummary|Hydrostatic Balance Equation]]</li>
<li>&clubs; [[SSCpt2/SolutionStrategies|Solution Strategies]]</li>
<li>[[SSC/SynopsisStyleSheet|Spherical Structures Synopsis]]   ⇐   Image of 1st page of synopsis</li>
<li>&clubs; Scalar Virial Theorem; subsection of ''Context'' - §VI [[VE#Scalar_Virial_Theorem|(Global Energy Considerations)]]</li>
<li>&clubs; [[SSC/Structure/UniformDensity|Uniform-Density Sphere]]</li>
<li>[[SSC/Structure/IsothermalSphere|Isothermal Sphere]]</li>
<li>Via Direct Numerical Integration; subsection of ''Equilibrium Structures'' - §VI [[SSC/Structure/IsothermalSphere#Our_Numerical_Integration|(Isothermal Sphere)]]</li>
<li>[[SSC/Structure/Polytropes|Isolated Polytropes]]</li>
<li>Known Analytic Solutions; subsection of ''Equilibrium Structures'' - §VIII [[SSC/Structure/Polytropes#Known_Analytic_Solutions|(Isolated Polytropes)]]</li>
<li>Via Direct Numerical Integration; subsection of ''Equilibrium Structures'' - §VIII [[SSC/Structure/Polytropes#Straight_Numerical_Integration|(Isolated Polytropes)]]</li>
<li>Via Self-Consistent Field (SCF) Technique; subsection of ''Equilibrium Structures'' - §VIII [[SSC/Structure/Polytropes#HSCF_Technique|(Isolated Polytropes)]]</li>
</ol>

=See Also=

JETohlineWiki - User contributions [en]

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