Difference between revisions of "User:Tohline/Appendix/Ramblings/RiemannB74C692"

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=Another S-type Example b74c692=
=Another S-type Example b74c692=


This chapter is an extension of the chapter we have titled, "[[User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA & Oculus Rift S]]."  Other closely related chapters are listed below under the heading, "[[#See_Also|See Also]]".
This chapter is an extension of the chapter we have titled, "[[User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA &amp; Oculus Rift S]]." In that chapter we used as our first example of a Riemann S-type ellipsoid the model with parameters, <b>b41c385</b>. Other closely related chapters are listed below under the heading, "[[#See_Also|See Also]]".


{{LSU_HBook_header}}
==Key Physical Parameters==
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 [[User:Tohline/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="5">
<b>Figure 1a</b><br />
[[File:EFE_STypeRiemannDiagram05.png|325px|EFE Parameter Space]]
  </td>
  <td align="center" rowspan="5" width="2%">
&nbsp;
  </td>
  <td align="center" colspan="3">
<math>~\frac{b}{a} = 0.41</math>
  </td>
  <td align="center" rowspan="5" width="2%">
&nbsp;
  </td>
  <td align="center" rowspan="5" bgcolor="lightgrey">
<b>Figure 1b</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="3">
&nbsp;
  </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>
</table>
The subscript "EFE" on &Omega; and &lambda; means that the relevant frequency is given in units that have been adopted in [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>.  In Figure 1a, the solid purple circular marker (where the pair of purple lines cross) identifies the location of this model in the "c/a versus b/a" diagram that appears as Figure 2 on p. 902 of [http://adsabs.harvard.edu/abs/1965ApJ...142..890C S. Chandrasekhar (1965)]; essentially the same diagram appears in &sect;49 (p. 147) of [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>]. 


{{LSU_HBook_header}}


=See Also=
=See Also=

Revision as of 02:45, 29 May 2020

Another S-type Example b74c692

This chapter is an extension of the chapter we have titled, "Riemann Meets COLLADA & Oculus Rift S." In that chapter we used as our first example of a Riemann S-type ellipsoid the model with parameters, b41c385. Other closely related chapters are listed below under the heading, "See Also".

Whitworth's (1981) Isothermal Free-Energy Surface
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Key Physical Parameters

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 Table 2 of our accompanying discussion of Riemann S-type ellipsoids:

Figure 1a
EFE Parameter Space

 

<math>~\frac{b}{a} = 0.41</math>

 

Figure 1b
EFE Model b41c385

<math>~\frac{c}{a} = 0.385</math>

Direct

 

Adjoint

<math>~\Omega_\mathrm{EFE} = 0.547874</math>

<math>~\Omega_\mathrm{EFE} = - 0.079886</math>

<math>~\lambda_\mathrm{EFE} = 0.079886</math>

<math>~\lambda_\mathrm{EFE} = - 0.547874</math>

The subscript "EFE" on Ω and λ means that the relevant frequency is given in units that have been adopted in [EFE], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>. In Figure 1a, the solid purple circular marker (where the pair of purple lines cross) identifies the location of this model in the "c/a versus b/a" diagram that appears as Figure 2 on p. 902 of S. Chandrasekhar (1965); essentially the same diagram appears in §49 (p. 147) of [EFE].


See Also


Whitworth's (1981) Isothermal Free-Energy Surface

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