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

From VistrailsWiki
Jump to navigation Jump to search
Line 1: Line 1:
<!-- __FORCETOC__ will force the creation of a Table of Contents -->
__FORCETOC__
<!-- __NOTOC__ will force TOC off -->
<!-- __NOTOC__ will force TOC off -->
=Another S-type Example b74c692=
=Another S-type Example b74c692=
Line 70: Line 70:


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


=See Also=
=See Also=

Revision as of 19:30, 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, (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
|   Tiled Menu   |   Tables of Content   |  Banner Video   |  Tohline Home Page   |

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} = 0.74</math>

 

Figure 1b
EFE Model b74c692

<math>~\frac{c}{a} = 0.692</math>

Direct

 

Adjoint

<math>~\Omega_\mathrm{EFE} = 0.638747</math>

<math>~\Omega_\mathrm{EFE} = - 0.217773</math>

<math>~\lambda_\mathrm{EFE} = 0.217773</math>

<math>~\lambda_\mathrm{EFE} = - 0.638747 </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].

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

© 2014 - 2021 by Joel E. Tohline
|   H_Book Home   |   YouTube   |
Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS |
Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation