Editing Appendix/Ramblings/RiemannB74C692 (section)

===rotation_euler_Z===
Whether the observer is viewing the system from an inertial frame of reference or a rotating frame of reference, this ''animation section'' specifies the rate at which the ellipsoid spins and the rate at which the "laboratory" is spinning.  Three sets of data must be specified:  
<ol>
<li>The "<font color="maroon">First</font>_rotation_euler_Z-input-array", which specifies TIME.</li>
<li>The "<font color="maroon">First</font>_rotation_euler_Z-output-array", which specifies how the ANGLE of orientation of the ellipsoid varies with TIME.</li>
<li>The "<font color="maroon">Frame</font>_rotation_euler_Z-output-array", which specifies how the spin ANGLE of the laboratory frame varies with TIME.</li>
</ol>

We have chosen to specify the time-varying angle in increments of 60&deg; and to end the animation sequence after the ellipsoid (or, alternatively, the laboratory frame) has completed exactly <b>five</b> full spins.  As a result &#8212; ignoring any zero-point offsets &#8212; one of the ANGLE arrays will vary from 0&deg; to 5 &times; 360&deg; = 1800&deg; in 60&deg; intervals (if spinning counter-clock-wise) or will vary from 1800&deg; to 0&deg; in -60&deg; intervals (if spinning clock-wise).  Again ignoring any zero-point offset, all the data values in the other ANGLE array will be 0&deg;.  The number of discrete data values that must be specified for each of the three arrays is therefore, by choice, count = (1800/60)+1 = 31.

All we have left to do is specify the TIME interval that is equivalent to a 60&deg; turn of the ellipsoid, as viewed from the inertial frame of reference.  Given that one cycle of the wall-clock's "minute" hand represents a frequency of <math>~[\pi G \rho]^{1 / 2}</math> and, furthermore by choice, we equate one cycle of the wall-clock's "minute" hand to TIME = 4 in COLLADA time units (approximately 4 seconds of real time), we know that <b>one</b> complete spin of the ellipsoid is  equivalent to 4/|&Omega;<sub>EFE</sub>| units of TIME.  Hence the ellipsoid will turn through 60&deg; in a time, &Delta;T<sub>&Omega;</sub> = 4/[6|&Omega;<sub>EFE</sub>|] and it will take TIME = 20/|&Omega;<sub>EFE</sub>| to complete five full spins.

<table border="1" align="center" cellpadding="8">
<tr>
<th align="center" colspan="4">''Direct''</th>
</tr>
<tr>
  <td align="center">Model</td>
  <td align="center">&Omega;<sub>EFE</sub></td>
  <td align="center">&Delta;T<sub>&Omega;</sub></td>
  <td align="center">5 Spins</td>
</tr>
<tr>
  <td align="center">b41c385</td>
  <td align="center">0.547874</td>
  <td align="center">1.2168</td>
  <td align="center">36.505</td>
</tr>
<tr>
  <td align="center" bgcolor="lightblue">b74c692</td>
  <td align="center" bgcolor="lightblue">0.638747</td>
  <td align="center" bgcolor="lightblue">1.0437</td>
  <td align="center" bgcolor="lightblue">31.311</td>
</tr>
<tr>
  <td align="center">b90c333</td>
  <td align="center">0.447158</td>
  <td align="center">1.4909</td>
  <td align="center">44.727</td>
</tr>
<tr>
  <td align="center">b28c256</td>
  <td align="center">0.456676</td>
  <td align="center">1.4598</td>
  <td align="center">43.795</td>
</tr>
</table>