ThreeDimensionalConfigurations/ChallengesPt5 - Revision history

Jet53man at 21:50, 15 April 2022

2022-04-15T21:50:48Z

Jet53man: /* See Also */

2022-02-17T23:41:48Z

See Also

← Older revision		Revision as of 19:41, 17 February 2022
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	=See Also=		=See Also=
	* [[~~User:Tohline~~/ThreeDimensionalConfigurations/RiemannTypeI#Riemann_Type_1_Ellipsoids\|Riemann Type 1 Ellipsoids]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/Challenges#Challenges_Constructing_Ellipsoidal-Like_Configurations\|Construction Challenges (Pt. 1)]]		* [[ThreeDimensionalConfigurations/DescriptionOfRiemannTypeI\|Description of Riemann Type I Ellipsoids]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt2\|Construction Challenges (Pt. 2)]]		* [[ThreeDimensionalConfigurations/RiemannTypeI#Riemann_Type_1_Ellipsoids\|Riemann Type 1 Ellipsoids]] (old introduction)
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt3\|Construction Challenges (Pt. 3)]]		* [[ThreeDimensionalConfigurations/Challenges#Challenges_Constructing_Ellipsoidal-Like_Configurations\|Construction Challenges (Pt. 1)]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt4\|Construction Challenges (Pt. 4)]]		* [[ThreeDimensionalConfigurations/ChallengesPt2\|Construction Challenges (Pt. 2)]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt5\|Construction Challenges (Pt. 5)]]		* [[ThreeDimensionalConfigurations/ChallengesPt3\|Construction Challenges (Pt. 3)]]
			* [[ThreeDimensionalConfigurations/ChallengesPt4\|Construction Challenges (Pt. 4)]]
			* [[ThreeDimensionalConfigurations/ChallengesPt5\|Construction Challenges (Pt. 5)]]
			* [[ThreeDimensionalConfigurations/ChallengesPt6\|Construction Challenges (Pt. 6)]]

	* Related discussions of models viewed from a rotating reference frame:		* Related discussions of models viewed from a rotating reference frame:
	** [[~~User:Tohline/~~PGE/RotatingFrame#Rotating_Reference_Frame\|PGE]]		** [[PGE/RotatingFrame#Rotating_Reference_Frame\|PGE]]
	** <font color="red"><b>NOTE to Eric Hirschmann & David Neilsen... </b></font>I have moved the earlier contents of this page to a new Wiki location called [[~~User:Tohline/~~Apps/RiemannEllipsoids_Compressible\|Compressible Riemann Ellipsoids]].		** <font color="red"><b>NOTE to Eric Hirschmann & David Neilsen... </b></font>I have moved the earlier contents of this page to a new Wiki location called [[Apps/RiemannEllipsoids_Compressible\|Compressible Riemann Ellipsoids]].


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Jet53man: Created page with "FORCETOC =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 5)= T..."

2021-07-24T22:32:46Z

Created page with "__FORCETOC__  =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 5)= T..."

Show changes

← Older revision		Revision as of 19:41, 17 February 2022
Line 1,218:		Line 1,218:

	=See Also=		=See Also=
	* [[~~User:Tohline~~/ThreeDimensionalConfigurations/RiemannTypeI#Riemann_Type_1_Ellipsoids\|Riemann Type 1 Ellipsoids]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/Challenges#Challenges_Constructing_Ellipsoidal-Like_Configurations\|Construction Challenges (Pt. 1)]]		* [[ThreeDimensionalConfigurations/DescriptionOfRiemannTypeI\|Description of Riemann Type I Ellipsoids]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt2\|Construction Challenges (Pt. 2)]]		* [[ThreeDimensionalConfigurations/RiemannTypeI#Riemann_Type_1_Ellipsoids\|Riemann Type 1 Ellipsoids]] (old introduction)
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt3\|Construction Challenges (Pt. 3)]]		* [[ThreeDimensionalConfigurations/Challenges#Challenges_Constructing_Ellipsoidal-Like_Configurations\|Construction Challenges (Pt. 1)]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt4\|Construction Challenges (Pt. 4)]]		* [[ThreeDimensionalConfigurations/ChallengesPt2\|Construction Challenges (Pt. 2)]]
	* [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt5\|Construction Challenges (Pt. 5)]]		* [[ThreeDimensionalConfigurations/ChallengesPt3\|Construction Challenges (Pt. 3)]]
			* [[ThreeDimensionalConfigurations/ChallengesPt4\|Construction Challenges (Pt. 4)]]
			* [[ThreeDimensionalConfigurations/ChallengesPt5\|Construction Challenges (Pt. 5)]]
			* [[ThreeDimensionalConfigurations/ChallengesPt6\|Construction Challenges (Pt. 6)]]

	* Related discussions of models viewed from a rotating reference frame:		* Related discussions of models viewed from a rotating reference frame:
	** [[~~User:Tohline/~~PGE/RotatingFrame#Rotating_Reference_Frame\|PGE]]		** [[PGE/RotatingFrame#Rotating_Reference_Frame\|PGE]]
	** <font color="red"><b>NOTE to Eric Hirschmann & David Neilsen... </b></font>I have moved the earlier contents of this page to a new Wiki location called [[~~User:Tohline/~~Apps/RiemannEllipsoids_Compressible\|Compressible Riemann Ellipsoids]].		** <font color="red"><b>NOTE to Eric Hirschmann & David Neilsen... </b></font>I have moved the earlier contents of this page to a new Wiki location called [[Apps/RiemannEllipsoids_Compressible\|Compressible Riemann Ellipsoids]].


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← Older revision		Revision as of 17:50, 15 April 2022
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	=Challenges Constructing Ellipsoidal-Like Configurations (Pt. 5)=		=Challenges Constructing Ellipsoidal-Like Configurations (Pt. 5)=

	This chapter extends the accompanying chapters titled, [[~~User:Tohline/~~ThreeDimensionalConfigurations/Challenges\|''Construction Challenges (Pt. 1)'']], [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt2\|''(Pt. 2)'']], [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt3\|''(Pt. 3)'']], and [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt4\|''(Pt. 4)'']].		This chapter extends the accompanying chapters titled, [[ThreeDimensionalConfigurations/Challenges\|''Construction Challenges (Pt. 1)'']], [[ThreeDimensionalConfigurations/ChallengesPt2\|''(Pt. 2)'']], [[ThreeDimensionalConfigurations/ChallengesPt3\|''(Pt. 3)'']], and [[ThreeDimensionalConfigurations/ChallengesPt4\|''(Pt. 4)'']].

	==Tilted Plane Intersects Ellipsoid==		==Tilted Plane Intersects Ellipsoid==

	In a [[~~User:Tohline/~~ThreeDimensionalConfigurations/RiemannTypeI#TippedPlane\|an early subsection of the accompanying discussion]], we have pointed out that the intersection of each Lagrangian fluid element's tipped orbital plane with the surface of the (purple) ellipsoidal surface is given by the (unprimed) body-frame coordinates that simultaneously satisfy the expressions,		In a [[ThreeDimensionalConfigurations/RiemannTypeI#TippedPlane\|an early subsection of the accompanying discussion]], we have pointed out that the intersection of each Lagrangian fluid element's tipped orbital plane with the surface of the (purple) ellipsoidal surface is given by the (unprimed) body-frame coordinates that simultaneously satisfy the expressions,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	[[File:RiemannType1Tipped01.gif\|center\|600px\|Animation of Intersection Curves]]		[[File:RiemannType1Tipped01.gif\|center\|600px\|Animation of Intersection Curves]]

	As it turns out — see our [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt4#Tipped_Plane\|accompanying discussion]] — this expression can be rewritten as,		As it turns out — see our [[ThreeDimensionalConfigurations/ChallengesPt4#Tipped_Plane\|accompanying discussion]] — this expression can be rewritten as,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</tr>		</tr>
	</table>		</table>
	demonstrating that, as viewed from the x'-y' plane, the (light-blue) intersection curve is always an off-center ellipse. See also our [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt2#COLLADA-Based_Representation\|COLLADA-based representation]] of these curves.		demonstrating that, as viewed from the x'-y' plane, the (light-blue) intersection curve is always an off-center ellipse. See also our [[ThreeDimensionalConfigurations/ChallengesPt2#COLLADA-Based_Representation\|COLLADA-based representation]] of these curves.

	==Trajectory of Lagrangian Fluid Elements==		==Trajectory of Lagrangian Fluid Elements==

	This subsection borrows heavily from [[~~User:Tohline/~~ThreeDimensionalConfigurations/ChallengesPt4#Step4\|an accompanying discussion]].		This subsection borrows heavily from [[ThreeDimensionalConfigurations/ChallengesPt4#Step4\|an accompanying discussion]].

	===Old Way of Thinking===		===Old Way of Thinking===
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	* Related discussions of models viewed from a rotating reference frame:		* Related discussions of models viewed from a rotating reference frame:
	** [[PGE/RotatingFrame#Rotating_Reference_Frame\|PGE]]		** [[PGE/RotatingFrame#Rotating_Reference_Frame\|PGE]]
	** <font color="red"><b>NOTE to Eric Hirschmann & David Neilsen... </b></font>I have moved the earlier contents of this page to a new Wiki location called [[Apps/~~RiemannEllipsoids_Compressible~~\|Compressible Riemann Ellipsoids]].		** <font color="red"><b>NOTE to Eric Hirschmann & David Neilsen... </b></font>I have moved the earlier contents of this page to a new Wiki location called [[Apps/RiemannEllipsoidsCompressible\|Compressible Riemann Ellipsoids]].


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ThreeDimensionalConfigurations/ChallengesPt5 - Revision history

Jet53man at 21:50, 15 April 2022

Jet53man: /* See Also */

Jet53man: Created page with "__FORCETOC__ =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 5)= T..."

Jet53man: Created page with "FORCETOC =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 5)= T..."