User:Tohline/Appendix/Ramblings/RiemannB74C692

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, b41c385. 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} = 0.74</math>				Figure 1b
		<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

• 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