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Appendix/Ramblings/COLLADA/RiemannSType|
2024-07-04T18:09:45Z

Created page with "  =For Shangli Ou= In order to download any one of (a selected subset of) the COLLADA-based model files referenced below, go to … <table border="3" align="center" cellpadding="10"><tr><td align="center" bgcolor="red"> <table border="0" cellpadding="8" align="center"> <tr> <td align="center"> Appendix/Ramblings/COLLADA/RiemannSType|<font color="white" size..."

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=For Shangli Ou=

In order to download any one of (a selected subset of) the COLLADA-based model files referenced below, go to …

<table border="3" align="center" cellpadding="10"><tr><td align="center" bgcolor="red">
<table border="0" cellpadding="8" align="center">
<tr>
<td align="center">
[[Appendix/Ramblings/COLLADA/RiemannSType|<font color="white" size="+1">DOWNLOADABLE 3D MODELS</font>]]
</td>
</tr>
</table>
</td></tr></table>

==EFE Diagram (Review)==

<table border="0" cellpadding="12" align="left"><tr><td align="center">'''Figure 1'''</td></tr><tr><td align="center">[[File:EFEdiagram4.png|left|400px|EFE Diagram identifying example models from Ou (2006)]]</td></tr></table>
In the context of our broad discussion of ellipsoidal figures of equilibrium, the label "EFE Diagram" refers to a two-dimensional parameter space defined by the pair of axis ratios (b/a, c/a), ''usually'' covering the ranges, 0 ≤ b/a ≤ 1 and 0 ≤ c/a ≤ 1. The classic/original version of this diagram appears as Figure 2 on p. 902 of {{ Chandrasekhar65_XXVfull }}; a somewhat less cluttered version appears on p. 147 of Chandrasekhar's [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>].

The version of the EFE Diagram shown here, on the left, highlights four model ''sequences'', all of which also can be found in the original version:
<ul>
<li>''Jacobi'' sequence — the smooth curve that runs through the set of small, dark-blue, diamond-shaped markers; the data identifying the location of these markers have been drawn from §39, Table IV of [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>]. The small red circular markers lie along this same sequence; their locations are taken from our own determinations, as detailed in [[ThreeDimensionalConfigurations/JacobiEllipsoids#Table2|Table 2]] of our accompanying discussion of Jacobi ellipsoids. All of the models along this sequence have <math>f \equiv \zeta/\Omega_f = 0</math> and are therefore solid-body rotators, that is, there is no internal motion when the configuration is viewed from a frame that is rotating with frequency, <math>\Omega_f</math>.</li>
<li>''Dedekind'' sequence — a smooth curve that lies precisely on top of the ''Jacobi'' sequence. Each configuration along this sequence is ''adjoint'' to a model on the ''Jacobi'' sequence that shares its (b/a, c/a) axis-ratio pair. All ellipsoidal figures along this sequence have <math>1/f = \Omega_f/\zeta = 0</math> and are therefore stationary as viewed from the ''inertial'' frame; the angular momentum of each configuration is stored in its internal motion (vorticity).</li>
<li>The X = -1 ''self-adjoint'' sequence — At every point along this sequence, the value of the key frequency ratio, <math>\zeta/\Omega_f</math>, in the ''adjoint'' configuration <math>(f_+)</math> is identical to the value of the frequency ratio in the ''direct'' configuration <math>(f_-)</math>; specifically, <math>f_+ = f_- = -(a^2+b^2)/(ab)</math>. The data identifying the location of the small, solid-black markers along this sequence have been drawn from §48, Table VI of [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>].</li>
<li>The X = +1 ''self-adjoint'' sequence — At every point along this sequence, the value of the key frequency ratio, <math>\zeta/\Omega_f</math>, in the ''adjoint'' configuration <math>(f_+)</math> is identical to the value of the frequency ratio in the ''direct'' configuration <math>(f_-)</math>; specifically, <math>f_+ = f_- = +(a^2+b^2)/(ab)</math>. The data identifying the location of the small, solid-black markers along this sequence have been drawn from §48, Table VI of [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>].</li>
</ul>

Riemann S-type ellipsoids all lie between or on the two (self-adjoint) curves marked "X = -1" and "X = +1" in the EFE Diagram. The yellow circular markers in the diagram shown here, on the left, identify four Riemann S-type ellipsoids that were examined by {{ Ou2006 }} and that we have also chosen to use as examples.

==Example 3D Interactive Animations==

For each model described below, note that,
<table border="0" cellpadding="5" align="center">

<tr>
<td align="right">
<math>f \equiv \frac{\zeta_\mathrm{EFE}}{\Omega_\mathrm{EFE}}</math>
</td>
<td align="center">
<math>=</math>
</td>
<td align="left">
<math>- \frac{\lambda_\mathrm{EFE}}{\Omega_\mathrm{EFE}} \biggl[ \frac{1+(b/a)^2}{b/a} \biggr] \, .</math>
</td>
</tr>
</table>

For additional details, see the [[ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS#The_COLLADA_Code_.26_Initial_3D_Scene|accompanying chapter titled, "Riemann Meets COLLADA & Oculus Rift S"]].

===b41c385===
The model that we have chosen to use in our first successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from [[ThreeDimensionalConfigurations/RiemannStype#Table2|Table 2 of our accompanying discussion of Riemann S-type ellipsoids]]:

<table border="0" cellpadding="5" align="center">

<tr>
<td align="center" rowspan="6">
<b>Figure 2a</b><br /> <br />
[[File:B41c385EFEdiagram02.png|325px|EFE Parameter Space]]
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" colspan="3">
<math>~\frac{b}{a} = 0.41</math>
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" rowspan="6" bgcolor="lightgrey">
<b>Figure 2b</b><br />
[[File:COLLADA3rdViewpoint.png|300px|EFE Model b41c385]]
</td>
</tr>

<tr>
<td align="center" colspan="3">
<math>~\frac{c}{a} = 0.385</math>
</td>
</tr>

<tr>
<td align="center">
''Direct''
</td>
<td align="center" width="2%" rowspan="4">
 
</td>
<td align="center">
''Adjoint''
</td>
</tr>

<tr>
<td align="center">
<math>~\Omega_\mathrm{EFE} = 0.547874</math>
</td>
<td align="center">
<math>~\Omega_\mathrm{EFE} = - 0.079886</math>
</td>
</tr>

<tr>
<td align="center">
<math>~\lambda_\mathrm{EFE} = 0.079886</math>
</td>
<td align="center">
<math>~\lambda_\mathrm{EFE} = - 0.547874</math>
</td>
</tr>

<tr>
<td align="center">
<math>~f = - 0.415418</math>
</td>
<td align="center">
<math>~f = - 19.53923</math>
</td>
</tr>
</table>

The subscript "EFE" on Ω and λ means that the relevant frequency is given in units that have been adopted in [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>. In Figure 2a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" ''[[ThreeDimensionalConfigurations/RiemannStype#Fig2|EFE Diagram]]'' that appears as Figure 2 on p. 902 of {{ Chandrasekhar65_XXV }}; essentially the same diagram appears in §49 (p. 147) of [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>].

In a [[ThreeDimensionalConfigurations/JacobiEllipsoids#Jacobi_Ellipsoids|separate chapter]] we have discussed various properties of uniformly rotating, ''Jacobi'' ellipsoids; they are equilibrium configurations that lie along the sequence that runs from "M<sub>2</sub>" (on the b/a = 1, Maclaurin sequence) to the origin of this diagram. Our chosen model lies off of — just above — the Jacobi-ellipsoid sequence, which means that it is not rotating as a solid body. Instead, as we focus first on the ''direct'' (as opposed to the ''adjoint'') configuration, we appreciate that while the ellipsoid is spinning prograde (counter-clockwise) with a frequency given by |Ω<sub>EFE</sub>|, each Lagrangian fluid element inside as well as on the surface of the ellipsoid is traveling retrograde (clockwise) along an elliptical path with a frequency given by |λ<sub>EFE</sub>|.

===b90c333===

The model that we have chosen to use in our second successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from [[ThreeDimensionalConfigurations/RiemannStype#Table2|Table 2 of our accompanying discussion of Riemann S-type ellipsoids]]:

<table border="0" cellpadding="5" align="center">

<tr>
<td align="center" rowspan="6">
<b>Figure 3a</b><br /> <br />
[[File:B90c333EFEdiagram02.png|325px|EFE Parameter Space]]
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" colspan="3">
<math>~\frac{b}{a} = 0.90</math>
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" rowspan="6" bgcolor="lightgrey">
<b>Figure 3b</b><br />
[[File:COLLADAb90c333NewModel.png|300px|EFE Model b90c333]]
</td>
</tr>

<tr>
<td align="center" colspan="3">
<math>~\frac{c}{a} = 0.333</math>
</td>
</tr>

<tr>
<td align="center">
''Direct''
</td>
<td align="center" width="2%" rowspan="4">
 
</td>
<td align="center">
''Adjoint''
</td>
</tr>

<tr>
<td align="center">
<math>~\Omega_\mathrm{EFE} = 0.447158</math>
</td>
<td align="center">
<math>~\Omega_\mathrm{EFE} = 0.221411</math>
</td>
</tr>

<tr>
<td align="center">
<math>~\lambda_\mathrm{EFE} = - 0.221411</math>
</td>
<td align="center">
<math>~\lambda_\mathrm{EFE} = - 0.447158 </math>
</td>
</tr>

<tr>
<td align="center">
<math>~f = + 0.995805</math>
</td>
<td align="center">
<math>~f = + 4.061607 </math>
</td>
</tr>
</table>

===b74c692===

The model that we have chosen to use in our third successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from [[ThreeDimensionalConfigurations/RiemannStype#Table2|Table 2 of our accompanying discussion of Riemann S-type ellipsoids]]:

<table border="0" cellpadding="5" align="center">

<tr>
<td align="center" rowspan="6">
<b>Figure 4a</b><br /> <br />
[[File:B74c692EFEdiagram02.png|325px|EFE Parameter Space]]
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" colspan="3">
<math>~\frac{b}{a} = 0.74</math>
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" rowspan="6" bgcolor="lightgrey">
<b>Figure 4b</b><br />
[[File:COLLADAb74c692NewModel.png|300px|EFE Model b74c692]]
</td>
</tr>

<tr>
<td align="center" colspan="3">
<math>~\frac{c}{a} = 0.692</math>
</td>
</tr>

<tr>
<td align="center">
''Direct''
</td>
<td align="center" width="2%" rowspan="4">
 
</td>
<td align="center">
''Adjoint''
</td>
</tr>

<tr>
<td align="center">
<math>~\Omega_\mathrm{EFE} = 0.638747</math>
</td>
<td align="center">
<math>~\Omega_\mathrm{EFE} = - 0.217773</math>
</td>
</tr>

<tr>
<td align="center">
<math>~\lambda_\mathrm{EFE} = 0.217773</math>
</td>
<td align="center">
<math>~\lambda_\mathrm{EFE} = - 0.638747 </math>
</td>
</tr>

<tr>
<td align="center">
<math>~f = - 0.713019</math>
</td>
<td align="center">
<math>~f = - 6.13413 </math>
</td>
</tr>
</table>

===b28c256===

The model that we have chosen to use in our second successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from [[ThreeDimensionalConfigurations/RiemannStype#Table2|Table 2 of our accompanying discussion of Riemann S-type ellipsoids]]:

<table border="0" cellpadding="5" align="center">

<tr>
<td align="center" rowspan="6">
<b>Figure 5a</b><br /> <br />
[[File:B28c256EFEdiagram02.png|325px|EFE Parameter Space]]
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" colspan="3">
<math>~\frac{b}{a} = 0.28</math>
</td>
<td align="center" rowspan="6" width="2%">
 
</td>
<td align="center" rowspan="6" bgcolor="lightgrey">
<b>Figure 5b</b><br />
[[File:COLLADAb28c256OldModel.png|300px|EFE Model b28c256]]
</td>
</tr>

<tr>
<td align="center" colspan="3">
<math>~\frac{c}{a} = 0.256</math>
</td>
</tr>

<tr>
<td align="center">
''Direct''
</td>
<td align="center" width="2%" rowspan="4">
 
</td>
<td align="center">
''Adjoint''
</td>
</tr>

<tr>
<td align="center">
<math>~\Omega_\mathrm{EFE} = 0.456676</math>
</td>
<td align="center">
<math>~\Omega_\mathrm{EFE} = - 0.020692</math>
</td>
</tr>

<tr>
<td align="center">
<math>~\lambda_\mathrm{EFE} = 0.020692</math>
</td>
<td align="center">
<math>~\lambda_\mathrm{EFE} = - 0.456676</math>
</td>
</tr>

<tr>
<td align="center">
<math>~f = - 0.174510</math>
</td>
<td align="center">
<math>~f = - 85.0007</math>
</td>
</tr>
</table>

=Catalog of Local 3D Model Files <font size="-1">(cannot be downloaded)</font>=
==3Dviewers==
===AutoRiemann===

<ul>
<li>
Trial.Ou_b28c256<br />
''Generally speaking ...'' Translucent surface; one Lagrangian (red surface arrow) fluid element; no axis arrow; NO WALL LABELs.
<ul>
<li>
<font color="maroon">Ou_b28c256.Dir.Inertial.dae</font> (12/01/2019)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">Ou_b28c256.Dir.Rot.dae</font> (12/01/2019)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">Ou_b28c256.Adj.Inertial.dae</font> (12/01/2019)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">Ou_b28c256.Adj.Rot.dae</font> (12/01/2019)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

<ul>
<li>
Cylinder<br />
''Generally speaking ...'' Translucent surface; one Lagrangian (red surface arrow) fluid element; no axis arrow; PROBLEM RESETING CLOCK.
<ul>
<li>
<font color="maroon">Dir.Inertial_b28c256.labeled.dae</font> (12/22/2019)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">Dir.Rot_b28c256.labeled.dae</font> (12/22/2019)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

<ul>
<li>
BESTmodels<br />
''Generally speaking ...'' Translucent surface; six Lagrangian (red arrow markers) fluid elements.
<ul>
<li>
<font color="maroon">b28c256/b28c256.DI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">b28c256/b28c256.DRot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">b28c256/b28c256.AI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">b28c256/b28c256.ARot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
 
<hr>
 
<li>
<font color="maroon">b41c385/b41c385.DI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.41~~~~~c/a = 0.385</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">b41c385/b41c385.DRot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.41 ~~~~~c/a = 0.385</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">b41c385/b41c385.AI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.41 ~~~~~c/a = 0.385</math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon">b41c385/b41c385.ARot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.41 ~~~~~c/a = 0.385</math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
 
<hr>
 
<li>
<font color="maroon">b74c692/b74c692.DI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.74~~~~~c/a = 0.692</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon"> b74c692/b74c692.DRot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.74 ~~~~~c/a = 0.692 </math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon"> b74c692/b74c692.AI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.74 ~~~~~c/a = 0.692 </math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon"> b74c692/b74c692.ARot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.74 ~~~~~c/a = 0.692 </math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
 
<hr>
 
<li>
<font color="maroon">b90c333/b90c333.DI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.90~~~~~c/a = 0.333</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon"> b90c333/b90c333.DRot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.90 ~~~~~c/a = 0.333 </math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon"> b90c333/b90c333.AI.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.90 ~~~~~c/a = 0.333 </math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
<li>
<font color="maroon"> b90c333/b90c333.ARot.dae</font> (01/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.90 ~~~~~c/a = 0.333 </math><br />'''<font color="red">ADJOINT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

<ul>
<li>
TypeI<br />
Translucent surface; just '''Type I tilted''' figure motion (no Lagrangian fluid elements).
<ul>
<li>
<font color="maroon">TypeIa10.GREAT.dae</font> (01/04/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 1.25~~~~~c/a = 0.470</math><br />'''<font color="red">DIRECT figure</font>''' (only) motion - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

<ul>
<li>
TypeI/Lagrange<br />
Depicts motion of (3) Lagrangian fluid elements across an opaque surface; no figure motion; three separate, tilted fluid orbits are identified by small yellow markers.
<ul>
<li>
<font color="maroon">TL15.lagrange.dae</font> (01/26/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 1.25~~~~~c/a = 0.470</math><br />'''<font color="red">LAGRANGIAN element</font>''' (only) motion - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

==Lenovo==

===KhronosGroup's COLLADA_to_gltf/COLLADA2GLTF-v2===

<ul>
<li>
ModelsB41C385<br />
Fundamentally this model is identical to the one developed earlier (and [[#b41c385|presented above]]) that shows how the ''DIRECT'' flow version of model "b41c385" appears when viewed from either the inertial or rotating reference frame: The ellipsoidal surface is purple [either translucent or opaque, as indicated]; the equatorial plane is identified by a series of small yellow markers; and 9 red markers depict the (slow, retrograde) Lagrangian motion of fluid elements that lie in the equatorial plane.
<ul>
<li>
<font color="maroon">MultiFluidElements/MultiLagrange26.dae</font> [translucent purple] (05/28/2020) and <font color="orange">/output/MultiLagrange26.glb</font> (06/04/2020) — both files also copied (01/31/2021) to LSU physics website with filename … COLLADA/b41c385DirRotating.
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.41~~~~~c/a = 0.385</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
<ul>
<li>
<font color="maroon">InertialFrame/Inertial34.dae</font> [opaque purple] (05/29/2020) and <font color="orange">/output/Inertial34.glb</font> (06/04/2020) — both files also copied (01/31/2021) to LSU physics website with filename … COLLADA/b41c385DirInertial.
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.41~~~~~c/a = 0.385</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

<ul>
<li>
ModelsB90C333<br />
Fundamentally this model is identical to the one developed earlier (and [[#b90c333|presented above]]) that shows how the ''DIRECT'' flow version of model "b90c333" appears when viewed from either the inertial or a rotating reference frame: The ellipsoidal surface is purple [either translucent or opaque, as indicated]; the equatorial plane is identified by a series of small yellow markers; and 9 red markers depict the (slow, prograde) Lagrangian motion of fluid elements that lie in the equatorial plane.
<ul>
<li>
<font color="maroon">FastRot79.dae</font> [translucent purple] (06/03/2020) and <font color="orange">/output/FastRot79.glb</font> (06/04/2020) — both files also copied (01/31/2021) to LSU physics website with filename … COLLADA/b90c333DirRotating.
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.90~~~~~c/a = 0.333</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
<ul>
<li>
<font color="maroon">FastInertial80.dae</font> [opaque purple] (06/03/2020) — Also available is <font color="orange">../output/FastInertial80.glb</font> (06/04/2020) — both files also copied (01/31/2021) to LSU physics website with filename … COLLADA/b90c333DirInertial.
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.90~~~~~c/a = 0.333</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

<ul>
<li>
ModelsB74C692<br />
Fundamentally this model is identical to the one developed earlier (and [[#b74c692|presented above]]) that shows how the ''DIRECT'' flow version of model "b74c692" appears when viewed from the rotating reference frame: The ellipsoidal surface is translucent (purple); the equatorial plane is identified by a series of small yellow markers; and 9 red markers depict the (slow, retrograde) Lagrangian motion of fluid elements that lie in the equatorial plane.
<ul>
<li>
<font color="maroon">TestMulti74.dae</font> (06/03/2020) — Also available is <font color="orange">../output/TestMulti74.glb</font> (06/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.74~~~~~c/a = 0.692</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
<ul>
<li>
<font color="maroon">InertialB74C692aa.dae</font> [opaque purple] (06/02/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.74~~~~~c/a = 0.692</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

<ul>
<li>
(no subdirectory)<br />
Fundamentally this model is identical to the one developed earlier (and [[#b28c256|presented above]]) that shows how the ''DIRECT'' flow version of model "b28c256" appears when viewed from the inertial reference frame: The ellipsoidal surface is purple [either translucent or opaque, as indicated]; the equatorial plane is identified by a series of small yellow markers; and 9 red markers depict the (very slow, retrograde) Lagrangian motion of fluid elements that lie in the equatorial plane.
<ul>
<li>
<font color="maroon">Pencil94.dae</font> [translucent purple surface] (06/04/2020) and <font color="orange">/output/Pencil94.glb</font> (06/04/2020) — both files also copied (01/30/2021) to LSU physics website with filename … COLLADA/b28c256DirRotating.
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">ROTATING</font>''' frame</div>
</td></tr></table>
</li>
</ul>
<ul>
<li>
<font color="maroon">PencilInertial96.dae</font> [opaque purple surface] (06/04/2020) and <font color="orange">/output/PencilInertial95.glb</font> (06/04/2020) — both files also copied (01/30/2021) to LSU physics website with filename … COLLADA/b28c256DirInertial.
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.28~~~~~c/a = 0.256</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

==Workfolder==
===Wiki_edits===

<ul>
<li>
CoordinateSystems<br />
Fundamentally this model is identical to the one developed earlier (and [[#b41c385|presented above]]) that shows how the ''DIRECT'' flow version of model "b41c385" appears when viewed from the inertial reference frame: The ellipsoidal surface is translucent (purple); the equatorial plane is identified by a series of small yellow markers; and a single, red marker depicts the (slow, retrograde) Lagrangian motion of one fluid element that lies in the equatorial plane.

But here, in addition across the "northern" hemisphere of the ellipsoid, a sequence of small yellow markers is used to identify the location of one <math>~\lambda_3</math> coordinate curve as defined within our so-called [[User:Tohline/Appendix/Ramblings/ConcentricEllipsodalT8Coordinates#Concentric_Ellipsoidal_.28T8.29_Coordinates|"T8" coordinate system]].
<ul>
<li>
<font color="maroon">Lambda3Curve03.dae</font> (12/26/2020)
<table border="1" cellpadding="8" align="center" width="50%"><tr><td align="left">
<div align="center"><math>~b/a = 0.41~~~~~c/a = 0.385</math><br />'''<font color="red">DIRECT</font>''' flow - as viewed from '''<font color="red">INERTIAL</font>''' frame</div>
</td></tr></table>
</li>
</ul>
</li>
</ul>

=See Also=

* Discussion of [[ThreeDimensionalConfigurations/RiemannStype|Ou's Riemann-Like Ellipsoids]]

* [[ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA & Oculus Rift S]]: Example <b>(b/a, c/a) = (0.41, 0.385)</b>
[[Appendix/Ramblings/VirtualReality#Virtual_Reality_and_3D_Printing|Virtual Reality and 3D Printing]]
[[Appendix/Ramblings/OculusRiftS|Success Importing Animated Scene into Oculus Rift S]]
[[Appendix/Ramblings/RiemannMeetsOculus|Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment]]
Other Example S-type Riemann Ellipsoids:
* <b>[[Appendix/Ramblings/RiemannB90C333|(b/a, c/a) = (0.90, 0.333)]]</b>
* <b>[[Appendix/Ramblings/RiemannB74C692|(b/a, c/a) = (0.74, 0.692)]]</b>
*** <b>[[Appendix/Ramblings/RiemannB28C256|(b/a, c/a) = (0.28, 0.256)]]</b>

{{ SGFfooter }}

Appendix/Ramblings/ForOuShangli - Revision history

Joel2: /* Wiki_edits */

← Older revision		Revision as of 14:23, 4 July 2024
Line 647:		Line 647:
	Fundamentally this model is identical to the one developed earlier (and [[#b41c385\|presented above]]) that shows how the ''DIRECT'' flow version of model "b41c385" appears when viewed from the inertial reference frame: The ellipsoidal surface is translucent (purple); the equatorial plane is identified by a series of small yellow markers; and a single, red marker depicts the (slow, retrograde) Lagrangian motion of one fluid element that lies in the equatorial plane.		Fundamentally this model is identical to the one developed earlier (and [[#b41c385\|presented above]]) that shows how the ''DIRECT'' flow version of model "b41c385" appears when viewed from the inertial reference frame: The ellipsoidal surface is translucent (purple); the equatorial plane is identified by a series of small yellow markers; and a single, red marker depicts the (slow, retrograde) Lagrangian motion of one fluid element that lies in the equatorial plane.

	But here, in addition across the "northern" hemisphere of the ellipsoid, a sequence of small yellow markers is used to identify the location of one <math>~\lambda_3</math> coordinate curve as defined within our so-called [[~~User:Tohline/~~Appendix/Ramblings/~~ConcentricEllipsodalT8Coordinates#Concentric_Ellipsoidal_.28T8.29_Coordinates~~\|"T8" coordinate system]].		But here, in addition across the "northern" hemisphere of the ellipsoid, a sequence of small yellow markers is used to identify the location of one <math>~\lambda_3</math> coordinate curve as defined within our so-called [[Appendix/Ramblings/ConcentricEllipsoidalT8Coordinates\|"T8" coordinate system]].
	<ul>		<ul>
	<li>		<li>