User:Tohline/Appendix/Ramblings/RiemannB90C333

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".

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		<math>~\frac{b}{a} = 0.90</math>				Figure 1b
		<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
  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

• Discussion of Ou's Riemann-Like Ellipsoids

• Riemann Meets COLLADA & Oculus Rift S
  • Virtual Reality and 3D Printing
  • Success Importing Animated Scene into Oculus Rift S
  • Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment: Example (b/a, c/a) = (0.41, 0.385)
  • Other Example S-type Riemann Ellipsoids:
    • (b/a, c/a) = (0.90, 0.333)
    • (b/a, c/a) = (0.74, 0.692)
    • (b/a, c/a) = (0.28, 0.256)

© 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