 # User:Tohline/Appendix/Ramblings/RiemannB90C333

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 Revision as of 10:51, 29 May 2020 (view source)Tohline (Talk | contribs) (→Key Physical Parameters)← Older edit Revision as of 11:09, 29 May 2020 (view source)Tohline (Talk | contribs) (→Key Physical Parameters)Newer edit → Line 28: Line 28:
Figure 1b
Figure 1b
- $~\Omega_\mathrm{EFE} = 0.638747$ + $~\Omega_\mathrm{EFE} = 0.447158$ - $~\Omega_\mathrm{EFE} = - 0.217773$ + $~\Omega_\mathrm{EFE} = 0.221411$
- $~\lambda_\mathrm{EFE} = 0.217773$ + $~\lambda_\mathrm{EFE} = - 0.221411$ - $~\lambda_\mathrm{EFE} = - 0.638747$ + $~\lambda_\mathrm{EFE} = - 0.447158$
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# 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: $~\frac{b}{a} = 0.90$ $~\frac{c}{a} = 0.333$ 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].