Difference between revisions of "User:Tohline/Appendix/Ramblings/RiemannB90C333"

From VistrailsWiki
Jump to navigation Jump to search
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>].
==Coding Steps==
Here we begin with a working model of [[User:Tohline/Appendix/Ramblings/RiemannB74C692#Another_S-type_Example_b74c692|b74c692]] and use incremental changes in the COLLADA-based code to construct a working model of b90c333.
<ul>
  <li>This pair of starting models has been copied from the successful modeling of Riemann S-type ellipsoids that have (b/a, c/a) = (0.74, 0.692)</li>
  <ul>
  <li>Inertial Frame:  <font color="lightgreen">[KEEP]</font> InertialB74C692aa.dae [02 May 2020]</li>
  <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> TestMulti74.dae [02 June 2020]</li>
  </ul>
  <li><font color="darkgreen"><b>FastRot74.dae</b></font></li>
</ul>
===Best b90c333 Models===
The example models created for display in the Oculus Rift S are the following:
<ol>
  <li>Inertial Frame:  </li>
  <li>Rotating Frame:  </li>
</ol>


=See Also=
=See Also=

Revision as of 19:59, 3 June 2020

Another S-type Example b90c333

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) = (0.90, 0.333). 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} = 0.90</math>

 

Figure 1b
EFE Model b90c333

<math>~\frac{c}{a} = 0.333</math>

Direct

 

Adjoint

<math>~\Omega_\mathrm{EFE} = 0.447158</math>

<math>~\Omega_\mathrm{EFE} = 0.221411</math>

<math>~\lambda_\mathrm{EFE} = - 0.221411</math>

<math>~\lambda_\mathrm{EFE} = - 0.447158 </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].

Coding Steps

Here we begin with a working model of b74c692 and use incremental changes in the COLLADA-based code to construct a working model of b90c333.

  • This pair of starting models has been copied from the successful modeling of Riemann S-type ellipsoids that have (b/a, c/a) = (0.74, 0.692)
    • Inertial Frame: [KEEP] InertialB74C692aa.dae [02 May 2020]
    • Rotating Frame: [KEEP] TestMulti74.dae [02 June 2020]
  • FastRot74.dae

Best b90c333 Models

The example models created for display in the Oculus Rift S are the following:

  1. Inertial Frame:
  2. Rotating Frame:


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