Editing H BookTiledMenu (section)

==Three-Dimensional Configurations==
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! style="height: 50px; width: 800px; background-color:lightgrey;"|<font color="navy" size="+2">(Initially) Three-Dimensional Configurations</font>
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<p>&nbsp;</p>

===Equilibrium Structures===
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! style="height: 30px; width: 800px; background-color:lightgrey;"|<font color="white" size="+1">3D STRUCTURE</font>
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<font color="darkgreen">"One interesting aspect of our models &hellip; is the pulsation characteristic of the final central triaxial figure &hellip; our interest in the pulsations  stems from a general concern about the equilibrium structure of self-gravitating, triaxial objects.  In the past, attempts to construct hydrostatic models of any equilibrium, triaxial structure having both a high <math>~T/|W|</math> value and a compressible equation of state have met with very limited success &hellip; they have been thwarted by a lack of understanding of how to represent complex internal motions in a physically realistic way&hellip; We suggest &hellip; that a ''natural'' attribute of [such] configurations may be pulsation and that, as a result, a search for simple circulation hydrostatic analogs of such systems may prove to a fruitless endeavor.</font>
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&#8212; Drawn from &sect;IVa of [https://ui.adsabs.harvard.edu/abs/1988ApJ...334..449W/abstract Williams &amp; Tohline (1988)], ApJ, 334, 449 
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Special numerical techniques must be developed <font color="darkgreen">"to build three-dimensional compressible equilibrium models with complicated flows."</font>  To date &hellip; <font color="darkgreen">"techniques have only been developed to build compressible equilibrium models of nonaxisymmetric configurations for a few systems with simplified rotational profiles, e.g., rigidly rotating systems ([https://ui.adsabs.harvard.edu/abs/1984PASJ...36..239H/abstract Hachisu &amp; Eriguchi 1984]; [https://ui.adsabs.harvard.edu/abs/1986ApJS...62..461H/abstract Hachisu 1986)], irrotational systems ([https://ui.adsabs.harvard.edu/abs/1998ApJS..118..563U/abstract Ury&#x016B; &amp; Eriguchi 1998]), and configurations that are stationary in the inertial frame ([https://ui.adsabs.harvard.edu/abs/1996MNRAS.282..653U/abstract Ury&#x016B; &amp; Eriguchi 1996])."</font>
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&#8212; Drawn from &sect;1 of {{ Ou2006full }} 
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====Ellipsoidal &amp; Ellipsoidal-Like====
&nbsp;

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! style="height: 150px; width: 150px; background-color:#9390DB;"|[[VE/RiemannEllipsoids|Steady-State<br />2<sup>nd</sup>-Order<br />Tensor Virial<br />Equations]]
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right: 2px solid black; " |<b>Uniform-Density<br />Incompressible<br />Ellipsoids</b>
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! style="height: 150px; width: 150px; background-color:#ffeeee;" |[[3Dconfigurations/RiemannEllipsoids|<b>Bernhard<br />Riemann<br />(1861)</b>]]
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<p>&nbsp;</p>

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! style="height: 150px; width: 150px; background-color:white; border-right: 2px dashed black; " |[[ThreeDimensionalConfigurations/HomogeneousEllipsoids|<b>The<br />Gravitational<br />Potential</b>]]<br />(A<sub>i</sub> coefficients)
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! style="height: 150px; width: 150px; background-color:#ffeeee; border-right: 2px dashed black; " |[[ThreeDimensionalConfigurations/JacobiEllipsoids#Jacobi_Ellipsoids|<b>Jacobi<br />Ellipsoids</b>]]
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! style="height: 150px; width: 150px; background-color:#ffeeee; border-right: 2px dashed black;" |[[ThreeDimensionalConfigurations/RiemannStype#Riemann_S-type_Ellipsoids|<b>Riemann<br />S-Type<br />Ellipsoids</b>]]
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! style="height: 150px; width: 150px; background-color:#ffeeee; border-right: 2px dashed black;" |[[3Dconfigurations/DescriptionOfRiemannTypeI|<b>Type I<br />Riemann<br />Ellipsoids</b>]]
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! style="height: 150px; width: 150px; background-color:white;" |[[ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|<b>Riemann<br />meets<br />COLLADA<br />&amp;<br /> Oculus Rift S</b>]]
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<p>&nbsp;</p>

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! style="height: 150px; width: 150px; background-color:white; border-right: 2px dashed black; " |[https://www.aimspress.com/article/10.3934/math.2019.2.215/fulltext.html <b>A Gauge Theory<br />of<br />Riemann Ellipsoids</b>]
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! style="height: 150px; width: 150px; background-color:white; " |[https://ui.adsabs.harvard.edu/abs/2020PhRvL.124e2501S/abstract <b>Nuclear<br />Wobbling Motion</b>]
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<p>&nbsp;</p>

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! style="height: 150px; width: 150px; background-color:#ffff99; border-right: 2px solid black; " |<b>Compressible<br />Analogs of<br />Riemann Ellipsoids</b>
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! style="height: 150px; width: 150px; background-color:#ffeeee; border-right: 2px dashed black;" |[[ThreeDimensionalConfigurations/FerrersPotential|<b>Ferrers<br />Potential<br />(1877)</b>]]
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! style="height: 150px; width: 150px; background-color:white; border-right: 2px dashed black;" |[https://ui.adsabs.harvard.edu/abs/2006ApJ...639..549O/abstract <b>Constructing<br />Ellipsoidal<br /> &amp; Ellipsoidal-Like<br />Configurations</b>]
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! style="height: 150px; width: 150px; background-color:white;" |[[ThreeDimensionalConfigurations/CAREs|<b>Thoughts<br />&amp;<br />Challenges</b>]]
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<p>&nbsp;</p>
* [https://ui.adsabs.harvard.edu/abs/1985Ap.....23..654K/abstract B. P. Kondrat'ev (1985)], Astrophysics, 23, 654:  ''Irrotational and zero angular momentum ellipsoids in the Dirichlet problem''
* {{ LRS93bfull }}:  ''Ellipsoidal Figures of Equilibrium:  Compressible models''

====Binary Systems====

* [https://ui.adsabs.harvard.edu/abs/1933MNRAS..93..539C/abstract S. Chandrasekhar (1933)], MNRAS, 93, 539:  ''The equilibrium of distorted polytropes.  IV. the rotational and the tidal distortions as functions of the density distribution''
* {{ Chandrasekhar63_XIXfull }}: ''The Equilibrium and the Stability of the Roche Ellipsoids''
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<td align="center" width="5%">&nbsp;</td><td align="left">
<font color="green">Roche's problem is concerned with the equilibrium and the stability of rotating homogeneous masses which are, further, distorted by the constant tidal action of an attendant rigid spherical mass.</font>
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===Stability Analysis===
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! style="height: 30px; width: 800px; background-color:lightgrey;"|<font color="white" size="+1">3D STABILITY</font>
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====Ellipsoidal &amp; Ellipsoidal-Like====
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<!-- |+ style="text-align:left; height:40px;" | <font size="+2">'''CONTEXT'''</font> -->
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! style="height: 150px; width: 150px; background-color:white; " |[[ThreeDimensionalConfigurations/Stability/RiemannEllipsoids|<b>Lebovitz &amp; Lifschitz (1996)</b>]]
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<p>&nbsp;</p>

====Binary Systems====

* {{ Chandrasekhar63_XIXfull }}:  ''The Equilibrium and the Stability of the Roche Ellipsoids''
* [https://ui.adsabs.harvard.edu/abs/2019ApJ...877....9H/abstract G. P. Horedt (2019)], ApJ, 877, 9:  ''On the Instability of Polytropic Maclaurin and Roche Ellipsoids''

===Nonlinear Evolution===
{| class="Chap18A" width=100% style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 3px; border-color:darkgrey;"
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! style="height: 30px; width: 800px; background-color:lightgrey;"|<font color="white" size="+1">3D DYNAMICS</font>
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<p>&nbsp;</p>
{| class="Chap18B" style="float:right; margin-left: 150px; border-style: solid; border-width: 3px; border-color:black;"
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! style="height: 150px; width: 320px; background-color:#D0FFFF;"|[[File:JacobiMaclaurin2.gif|320px|link=ThreeDimensionalConfigurations/EFE_Energies#Animation|Animation related to Fig. 3 from Christodoulou1995]]
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! style="height: 150px; width: 150px; background-color:#9390DB; border-left:2px solid black;"|[[ThreeDimensionalConfigurations/EFE_Energies#Properties_of_Homogeneous_Ellipsoids_.282.29|Free-Energy<br />Evolution<br />from the Maclaurin<br />to the Jacobi<br />Sequence]]
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{| class="Chap18C" style="margin-right: auto; margin-left: 75px; border-style: solid; border-width: 3px; border-color: black;"
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! style="height: 150px; width: 150px; background-color:#ffff99; border-right: 2px solid black; " |[[ThreeDimensionalConfigurations/BinaryFission#Fission_Hypothesis_of_Binary_Star_Formation|<b>Fission<br />Hypothesis</b>]]
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! style="height: 150px; width: 150px; background-color:white;" |[http://www.phys.lsu.edu/~tohline/fission.movies.html <b>"Fission"<br />Simulations<br />at LSU</b>]
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<p>&nbsp;</p>

====Secular====
* [https://ui.adsabs.harvard.edu/abs/1971ApJ...170..143F/abstract M. Fujimoto (1971)], ApJ, 170, 143:  ''Nonlinear Motions of Rotating Gaseous Ellipsoids''
* [https://ui.adsabs.harvard.edu/abs/1973ApJ...181..513P/abstract W. H. Press &amp; S. A. Teukolsky (1973)], ApJ, 181, 513:  ''On the Evolution of the Secularly Unstable, Viscous Maclaurin Spheroids''
* [https://ui.adsabs.harvard.edu/abs/1977ApJ...213..193D/abstract S. L. Detweiler &amp; L. Lindblom (1977)], ApJ, 213, 193:  ''On the evolution of the homogeneous ellipsoidal figures.''

====Dynamical====