Editing ThreeDimensionalConfigurations/ChallengesPt2 (section)

===COLLADA-Based Representation===

As has been described in an [[ThreeDimensionalConfigurations/RiemannTypeI#Figure3|accompanying discussion of Riemann Type 1 ellipsoids]], we have used COLLADA to construct  an animated and interactive 3D scene that displays in purple the surface of an example Type I ellipsoid; panels a and b of Figure 1 show what this ellipsoid looks like when viewed from two different perspectives.  (As a reminder &#8212; see the [[#explanation| explanation accompanying Figure 2 of that accompanying discussion]] &#8212; the ellipsoid is tilted about the x-coordinate axis at an angle of 61.25&deg; to the equilibrium spin axis, which is shown in green.)  Yellow markers also have been placed in this 3D scene at each of the coordinate locations specified in the [[#ExampleTrajectories|table that accompanies that discussion]].  From the perspective presented in Figure 3b, we can immediately identify three separate, nearly circular trajectories; the largest one corresponds to our choice of z<sub>0</sub> = -0.25, the smallest corresponds to our choice of z<sub>0</sub> = -0.60, and the one of intermediate size correspond to our choice of z<sub>0</sub> = -0.4310.  When viewed from the perspective presented in Figure 1a, we see that these three trajectories define three separate planes; each plane is tipped at an angle of &theta; = -19.02&deg; to the ''untilted'' equatorial, x-y plane of the purple ellipsoid.

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  <th align="center">Figure 1a</th>
  <th align="center">Figure 1b</th>
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[[File:B125c470B.cropped.png|500px|EFE Model b41c385]]
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[[File:B125c470A.cropped.png|500px|EFE Model b41c385]]
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[[File:DataFileButton02.png|75px|file = Dropbox/3Dviewers/AutoRiemann/TypeI/Lagrange/TL15.lagrange.dae]] <font size="+2">&#x21b2;</font>
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  <th align="center" colspan="2">Figure 1c</th>
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[[File:ProjectedOrbitsFlipped2.png|600px|EFE Model b41c385]]<br />
  <div align="center">[[File:DataFileButton02.png|75px|file = Dropbox/3Dviewers/RiemannModels/RiemannCalculations.xlsx --- worksheet = TypeI_1b]] <font size="+2">&#x21b2;</font></div>
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