ThreeDimensionalConfigurations/EFE Energies - Revision history

Jet53man: /* Conserve Only L */

2022-04-27T18:17:41Z

Conserve Only L

← Older revision		Revision as of 14:17, 27 April 2022
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	[[File:~~VisTrailsFig3e~~.png\|240px\|Both 2D contour plots overlaid]]		[[File:VisTrailsFig3f.png\|240px\|Both 2D contour plots overlaid]]
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Jet53man: /* Conserve Only L */

2022-04-27T17:56:16Z

Conserve Only L

← Older revision		Revision as of 13:56, 27 April 2022
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	Figure 3 of [http://adsabs.harvard.edu/abs/1995ApJ...446..472C Paper I] presents a black-and-white contour plot of this <math>~E_L</math> function for the specific case of <math>~L = 4.71488</math>, which, for reference, is the total angular momentum of an equilibrium [[~~User:Tohline/~~Apps/MaclaurinSpheroids#Maclaurin_Spheroids_.28axisymmetric_structure.29\|Maclaurin spheroid]] having an eccentricity, <math>~e = 0.85</math> (see [[#Table1\|Table 1, below]]). We have digitally extracted this black-and-white contour plot from p. 477 of the (PDF-formatted) [http://adsabs.harvard.edu/abs/1995ApJ...446..472C Paper I] publication and have reprinted it as the left-hand panel of our Figure 1. Note that we have flipped the plot horizontally and rotated it by 90° so that the orientation of the axis pair, <math>~(\tfrac{b}{a},\tfrac{c}{a})</math>, conforms with the orientation of a related, information-rich diagram presented by [https://ui.adsabs.harvard.edu/abs/1965ApJ...142..890C/abstract Chandrasekhar (1965)] — see also our [[~~User:Tohline/~~ThreeDimensionalConfigurations/JacobiEllipsoids#Sequence_Plots\|accompanying discussion of equilibrium sequence plots]].		Figure 3 of [http://adsabs.harvard.edu/abs/1995ApJ...446..472C Paper I] presents a black-and-white contour plot of this <math>~E_L</math> function for the specific case of <math>~L = 4.71488</math>, which, for reference, is the total angular momentum of an equilibrium [[Apps/MaclaurinSpheroids#Maclaurin_Spheroids_.28axisymmetric_structure.29\|Maclaurin spheroid]] having an eccentricity, <math>~e = 0.85</math> (see [[#Table1\|Table 1, below]]). We have digitally extracted this black-and-white contour plot from p. 477 of the (PDF-formatted) [http://adsabs.harvard.edu/abs/1995ApJ...446..472C Paper I] publication and have reprinted it as the left-hand panel of our Figure 1. Note that we have flipped the plot horizontally and rotated it by 90° so that the orientation of the axis pair, <math>~(\tfrac{b}{a},\tfrac{c}{a})</math>, conforms with the orientation of a related, information-rich diagram presented by [https://ui.adsabs.harvard.edu/abs/1965ApJ...142..890C/abstract Chandrasekhar (1965)] — see also our [[ThreeDimensionalConfigurations/JacobiEllipsoids#Sequence_Plots\|accompanying discussion of equilibrium sequence plots]].

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Jet53man: /* Free Energy of Incompressible, Constant Mass Systems */

2022-04-27T17:55:15Z

Free Energy of Incompressible, Constant Mass Systems

← Older revision		Revision as of 13:55, 27 April 2022
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	and the functional behavior of the coefficients, <math>~A_1</math>, <math>~A_2</math>, and <math>~A_3</math>, are given by the expressions provided in an [[~~User:Tohline/~~ThreeDimensionalConfigurations/HomogeneousEllipsoids#Evaluation_of_Coefficients\|accompanying discussion]].		and the functional behavior of the coefficients, <math>~A_1</math>, <math>~A_2</math>, and <math>~A_3</math>, are given by the expressions provided in an [[ThreeDimensionalConfigurations/HomogeneousEllipsoids#Evaluation_of_Coefficients\|accompanying discussion]].

Jet53man: /* Conserved Quantities */

2022-04-27T17:54:31Z

Conserved Quantities

← Older revision		Revision as of 13:54, 27 April 2022
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	[ 2<sup>nd</sup> expression — [https://ui.adsabs.harvard.edu/abs/1995ApJ...446..472C/abstract Paper I], <font color="#00CC00">Eq. (2.7)</font> ]<br />		[ 2<sup>nd</sup> expression — [https://ui.adsabs.harvard.edu/abs/1995ApJ...446..472C/abstract Paper I], <font color="#00CC00">Eq. (2.7)</font> ]<br />
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	where — see an [[~~User:Tohline/~~ThreeDimensionalConfigurations/HomogeneousEllipsoids#Triaxial_Configurations\|accompanying discussion]] for the definitions of <math>~A_1</math>, <math>~A_2</math>, and <math>~A_3</math>,		where — see an [[ThreeDimensionalConfigurations/HomogeneousEllipsoids#Triaxial_Configurations\|accompanying discussion]] for the definitions of <math>~A_1</math>, <math>~A_2</math>, and <math>~A_3</math>,

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174.64.14.12: Created page with " =Properties of Homogeneous Ellipsoids (2)= In addition to pulling..."

2021-09-30T23:00:47Z

Created page with "  =Properties of Homogeneous Ellipsoids (2)= In addition to pulling..."

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