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   <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> TestMulti74.dae [02 June 2020]</li>
   <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> TestMulti74.dae [02 June 2020]</li>
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   </ul>
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   <li><font color="darkgreen"><b>FastRot74.dae</b></font></li>
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   <li><font color="darkgreen"><b>FastRot74.dae</b></font>
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<br />Identical to <b>TestMulti74.dae</b> except wall-mounted labeling has been changed to reflect new values of b/a and c/a.
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   <li>Rotating Frame:  </li>
   <li>Rotating Frame:  </li>
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=See Also=
=See Also=

Revision as of 14:02, 3 June 2020

Contents

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
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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} = 0.90

 

Figure 1b
EFE Model b90c333

~\frac{c}{a} = 0.333

Direct

 

Adjoint

~\Omega_\mathrm{EFE} =  0.447158

~\Omega_\mathrm{EFE} =  0.221411

~\lambda_\mathrm{EFE} = - 0.221411

~\lambda_\mathrm{EFE} = - 0.447158

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].

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
    Identical to TestMulti74.dae except wall-mounted labeling has been changed to reflect new values of b/a and c/a.

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

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