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=Another S-type Example b74c692=
=Another S-type Example b74c692=


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]]".
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>(b/a, c/a) = (0.41, 0.385)</b>.  Here we construct a model with parameters, <b>(b/a, c/a) = (0.74, 0.692)</b>.  Other closely related chapters are listed below under the heading, "[[#See_Also|See Also]]".


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Revision as of 16:36, 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
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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

 

<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].

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

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