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=Another S-type Example b74c692=
=Another S-type Example b74c692=
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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>].
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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==COLLADA Model Files==
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<div align="center" id="Scroll1">
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<b>b74c692DI.dae</b> [''Direct'' Inertial Frame]&nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
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</div>
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<div style="height: 250px; width: 100%; overflow: scroll;">
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<pre>
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<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
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</pre>
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</div>
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<div align="center" id="Scroll2">
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<b>b74c692DRot.dae</b> [''Direct'' Rotating Frame]&nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
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</div>
 +
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<div style="height: 250px; width: 100%; overflow: scroll;">
 +
<pre>
 +
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
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</pre>
 +
</div>
 +
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<div align="center" id="Scroll3">
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<b>b74c692AI.dae</b> [''Adjunct'' Inertial Frame]&nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
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</div>
 +
 +
<div style="height: 250px; width: 100%; overflow: scroll;">
 +
<pre>
 +
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
 +
</pre>
 +
</div>
 +
 +
 +
<div align="center" id="Scroll4">
 +
<b>b74c692ARot.dae</b> [''Adjunct'' Rotating Frame]&nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
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</div>
 +
 +
<div style="height: 250px; width: 100%; overflow: scroll;">
 +
<pre>
 +
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
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</pre>
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</div>
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=See Also=
=See Also=

Revision as of 13:30, 29 May 2020

Contents

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, (b/a, c/a) = (0.41, 0.385). Here we construct a model with parameters, (b/a, c/a) = (0.74, 0.692). 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} = 0.74

 

Figure 1b
EFE Model b74c692

~\frac{c}{a} = 0.692

Direct

 

Adjoint

~\Omega_\mathrm{EFE} =  0.638747

~\Omega_\mathrm{EFE} = - 0.217773

~\lambda_\mathrm{EFE} = 0.217773

~\lambda_\mathrm{EFE} = - 0.638747

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].

COLLADA Model Files

b74c692DI.dae [Direct Inertial Frame]    …     a COLLADA code containing nnnn lines of <xml>-formatted ASCII text

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>


b74c692DRot.dae [Direct Rotating Frame]    …     a COLLADA code containing nnnn lines of <xml>-formatted ASCII text

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>


b74c692AI.dae [Adjunct Inertial Frame]    …     a COLLADA code containing nnnn lines of <xml>-formatted ASCII text

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>


b74c692ARot.dae [Adjunct Rotating Frame]    …     a COLLADA code containing nnnn lines of <xml>-formatted ASCII text

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>


See Also


Whitworth's (1981) Isothermal Free-Energy Surface

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