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, (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".
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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:
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Figure 1a |
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<math>~\frac{b}{a} = 0.74</math> |
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Figure 1b |
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<math>~\frac{c}{a} = 0.692</math> |
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Direct |
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Adjoint |
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<math>~\Omega_\mathrm{EFE} = 0.638747</math> |
<math>~\Omega_\mathrm{EFE} = - 0.217773</math> |
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<math>~\lambda_\mathrm{EFE} = 0.217773</math> |
<math>~\lambda_\mathrm{EFE} = - 0.638747 </math> |
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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].
COLLADA Model Files
b74c692DI.dae [Direct Inertial Frame] … a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
b74c692DRot.dae [Direct Rotating Frame] … a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
b74c692AI.dae [Adjunct Inertial Frame] … a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
b74c692ARot.dae [Adjunct Rotating Frame] … a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
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:
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© 2014 - 2021 by Joel E. Tohline |