Another S-type Example b28c256

User:Tohline/Appendix/Ramblings/RiemannB28C256

Key Physical Parameters

Coding Steps

COLLADA Model Files

Contents

Part A

Best b28c256 Models

Direct Configurations

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) = (0.28, 0.256). Other closely related chapters are listed below under the heading, "See Also".

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:

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 yellow circular marker, that has been placed where the pair of purple dashed 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].

Here we begin with a working model of b90c333 and use incremental changes in the COLLADA-based code to construct a working model of b28c256.

This pair of starting models has been copied from the successful modeling of Riemann S-type ellipsoids that have (b/a, c/a) = (0.90, 0.333)

Inertial Frame: [KEEP] FastInertial80.dae [04 June 2020]
Rotating Frame: [KEEP] FastRot79.dae [04 June 2020]

Pencil90.dae
Identical to FastRot79.dae except wall-mounted labeling has been changed to reflect new values of b/a and c/a. This works in both visualization venues.
Pencil91.dae
Inserted correct surface geometry of this rapidly rotating Riemann ellipsoid. This works in both visualization venues.
Pencil92.dae
Inserted the correct animated depiction of the 9 Lagrangian fluid elements.
Pencil93.dae
Placed 51 yellow, equatorial-plane markers. This works in both visualization venues
Pencil94.dae
Finished specifying correct behavior of clock, which gives the final, fully functional model. This works in both visualization venues
PencilInertial95.dae
Flipped from rotating- to inertial-frame of reference. This works in both visualization venues
PencilInertial96.dae
Enlarged red "Lagrange01" marker from 0.03 to 0.075; and changed transparency of ellipsoid surface to (totally opaque) 1.0. This works in both visualization venues

The example models created for display in the Oculus Rift S are the following:

Inertial Frame: [KEEP] PencilInertial96.dae [04 June 2020]
Rotating Frame: [KEEP] Pencil94.dae [04 June 2020]

b28c256DI.dae [Direct Inertial Frame] … a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
Original filename used above: xxx.dae

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>

b28c256DRot.dae [Direct Rotating Frame] … a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
Original filename used above: xxx.dae

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>

Figure 1a

<math>~\frac{b}{a} = 0.28</math>

Figure 1b

<math>~\frac{c}{a} = 0.256</math>

<math>~\Omega_\mathrm{EFE} = 0.456676</math>

<math>~\Omega_\mathrm{EFE} = - 0.020692</math>

<math>~\lambda_\mathrm{EFE} = 0.020692</math>

<math>~\lambda_\mathrm{EFE} = - 0.456676</math>

<math>~f = - 0.174510</math>

<math>~f = - 85.0007</math>