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=Another S-type Example b74c692=
=Another S-type Example b74c692=
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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]]".
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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]]".
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{{LSU_HBook_header}}
{{LSU_HBook_header}}
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==Key Physical Parameters==
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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]]:
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<table border="0" cellpadding="5" align="center">
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<tr>
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  <td align="center" rowspan="5">
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<b>Figure 1a</b><br />
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[[File:EFE_STypeRiemannDiagram05.png|325px|EFE Parameter Space]]
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  </td>
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  <td align="center" rowspan="5" width="2%">
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&nbsp;
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  </td>
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  <td align="center" colspan="3">
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<math>~\frac{b}{a} = 0.41</math>
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  </td>
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  <td align="center" rowspan="5" width="2%">
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&nbsp;
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  </td>
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  <td align="center" rowspan="5" bgcolor="lightgrey">
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<b>Figure 1b</b><br />
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[[File:COLLADA3rdViewpoint.png|300px|EFE Model b41c385]]
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  </td>
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</tr>
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<tr>
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  <td align="center" colspan="3">
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<math>~\frac{c}{a} = 0.385</math>
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  </td>
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</tr>
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<tr>
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  <td align="center">
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''Direct''
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  </td>
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  <td align="center" width="2%" rowspan="3">
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&nbsp;
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  </td>
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  <td align="center">
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''Adjoint''
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  </td>
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</tr>
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<tr>
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  <td align="center">
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<math>~\Omega_\mathrm{EFE} =  0.547874</math>
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  </td>
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  <td align="center">
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<math>~\Omega_\mathrm{EFE} = - 0.079886</math>
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  </td>
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</tr>
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<tr>
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  <td align="center">
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<math>~\lambda_\mathrm{EFE} = 0.079886</math>
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  </td>
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  <td align="center">
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<math>~\lambda_\mathrm{EFE} = - 0.547874</math>
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  </td>
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</tr>
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</table>
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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>]. 
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=See Also=
=See Also=

Revision as of 20:45, 28 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

 

~\frac{b}{a} = 0.41

 

Figure 1b
EFE Model b41c385

~\frac{c}{a} = 0.385

Direct

 

Adjoint

~\Omega_\mathrm{EFE} =  0.547874

~\Omega_\mathrm{EFE} = - 0.079886

~\lambda_\mathrm{EFE} = 0.079886

~\lambda_\mathrm{EFE} = - 0.547874

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 ~[\pi G\rho]^{1 / 2}. 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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