User:Tohline/ThreeDimensionalConfigurations/HomogeneousEllipsoids - Revision history

Tohline: /* Inhomogeneous Ellipsoids Leading to Ferrers Potentials */

2020-12-11T03:49:15Z

Inhomogeneous Ellipsoids Leading to Ferrers Potentials

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Tohline: /* See Also */

2020-12-11T03:46:52Z

Tohline: /* Inhomogeneous Ellipsoids Leading to Ferrers Potentials */

2020-12-10T03:08:41Z

Inhomogeneous Ellipsoids Leading to Ferrers Potentials

← Older revision		Revision as of 03:08, 10 December 2020
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	Other references to Ferrers Potential:		Other references to Ferrers Potential:
	<ul>		<ul>
	<li>Ferrers, N. M. (1877, Quarterly Journal of Pure and Applied Mathematics, 14, 1) … from [[User:Tohline/Appendix/References#BT87\|BT87]] References (p. 711)</li>		<li>[https://babel.hathitrust.org/cgi/pt?id=uc1.$b417536&view=1up&seq=15 Ferrers, N. M. (1877, Quarterly Journal of Pure and Applied Mathematics, 14, 1)] … from [[User:Tohline/Appendix/References#BT87\|BT87]] References (p. 711)</li>
	<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>		<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>
	<li>[https://www.mdpi.com/2075-4434/5/4/101 Lucas Antonio Caritá, Irapuan Rodriguez, & I. Puerari (2017)] <i>Explicit Second Partial Derivatives of the Ferrers Potential</i></li>		<li>[https://www.mdpi.com/2075-4434/5/4/101 Lucas Antonio Caritá, Irapuan Rodriguez, & I. Puerari (2017)] <i>Explicit Second Partial Derivatives of the Ferrers Potential</i></li>

Tohline: /* Inhomogeneous Ellipsoids Leading to Ferrers Potentials */

2020-12-10T03:02:55Z

Inhomogeneous Ellipsoids Leading to Ferrers Potentials

← Older revision		Revision as of 03:02, 10 December 2020
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	Other references to Ferrers Potential:		Other references to Ferrers Potential:
	<ul>		<ul>
			<li>Ferrers, N. M. (1877, Quarterly Journal of Pure and Applied Mathematics, 14, 1) … from [[User:Tohline/Appendix/References#BT87\|BT87]] References (p. 711)</li>
	<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>		<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>
	<li>[https://www.mdpi.com/2075-4434/5/4/101 Lucas Antonio Caritá, Irapuan Rodriguez, & I. Puerari (2017)] <i>Explicit Second Partial Derivatives of the Ferrers Potential</i></li>		<li>[https://www.mdpi.com/2075-4434/5/4/101 Lucas Antonio Caritá, Irapuan Rodriguez, & I. Puerari (2017)] <i>Explicit Second Partial Derivatives of the Ferrers Potential</i></li>

Tohline: /* Inhomogeneous Ellipsoids Leading to Ferrers Potentials */

2020-12-10T01:58:10Z

Inhomogeneous Ellipsoids Leading to Ferrers Potentials

← Older revision		Revision as of 01:58, 10 December 2020
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	<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>		<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>
	<li>[https://www.mdpi.com/2075-4434/5/4/101 Lucas Antonio Caritá, Irapuan Rodriguez, & I. Puerari (2017)] <i>Explicit Second Partial Derivatives of the Ferrers Potential</i></li>		<li>[https://www.mdpi.com/2075-4434/5/4/101 Lucas Antonio Caritá, Irapuan Rodriguez, & I. Puerari (2017)] <i>Explicit Second Partial Derivatives of the Ferrers Potential</i></li>
			<li>[https://www.researchgate.net/publication/225744594_Anisotropic_and_inhomogeneous_S-type_Riemann_ellipsoids_inside_spheroidal_halos_II Martin G. Abrahamyan (2006, Astrophysics, 49(3), 306-319)], ''Anisotropic and inhomogeneous S-type Riemann ellipsoids inside spheroidal halos. II''</li>
	</ul>		</ul>
	</td>		</td>

Tohline: /* Inhomogeneous Ellipsoids Leading to Ferrers Potentials */

2020-12-10T01:51:07Z

Inhomogeneous Ellipsoids Leading to Ferrers Potentials

← Older revision		Revision as of 01:51, 10 December 2020
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	<ul>		<ul>
	<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>		<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>
			<li>[https://www.mdpi.com/2075-4434/5/4/101 Lucas Antonio Caritá, Irapuan Rodriguez, & I. Puerari (2017)] <i>Explicit Second Partial Derivatives of the Ferrers Potential</i></li>
	</ul>		</ul>
	</td>		</td>

Tohline: /* Inhomogeneous Ellipsoids Leading to Ferrers Potentials */

2020-12-10T01:42:36Z

Inhomogeneous Ellipsoids Leading to Ferrers Potentials

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	=Inhomogeneous Ellipsoids Leading to Ferrers Potentials=		=Inhomogeneous Ellipsoids Leading to Ferrers Potentials=

			<table border="1" cellpadding="8" width="80%" align="center">
			<tr><td align="left">
			Other references to Ferrers Potential:
			<ul>
			<li>[https://docs.galpy.org/en/v1.6.0/reference/potentialferrers.html Galpy methods]</li>
			</ul>
			</td>
			</tr>
			</table>

	Following §2.3.2 (beginning on p. 60) of [[User:Tohline/Appendix/References#BT87\|BT87]], let's examine ''inhomogeneous'' configurations whose isodensity surfaces (including the surface, itself) are defined by triaxial ellipsoids on which the Cartesian coordinates <math>~(x_1, x_2, x_3)</math> satisfy the condition that,		Following §2.3.2 (beginning on p. 60) of [[User:Tohline/Appendix/References#BT87\|BT87]], let's examine ''inhomogeneous'' configurations whose isodensity surfaces (including the surface, itself) are defined by triaxial ellipsoids on which the Cartesian coordinates <math>~(x_1, x_2, x_3)</math> satisfy the condition that,

Tohline: /* When am = as */

2020-10-25T21:38:11Z

When am = as

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	==When a<sub>m</sub> = a<sub>s</sub>==		==When a<sub>m</sub> = a<sub>s</sub>==
	When the length of the intermediate axis is the same as the length of the shortest axis — that is, when we are dealing with ~~an oblate~~ spheroid — the coefficient associated with the longest axis is,		When the length of the intermediate axis is the same as the length of the shortest axis — that is, when we are dealing with a prolate spheroid — the coefficient associated with the longest axis is,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Tohline: /* When am = aℓ */

2020-10-25T21:37:47Z

When am = aℓ

← Older revision		Revision as of 21:37, 25 October 2020
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	==When a<sub>m</sub> = a<sub>ℓ</sub>==		==When a<sub>m</sub> = a<sub>ℓ</sub>==
	When the length of the intermediate axis is the same as the length of the longest axis — that is, when we are dealing with ~~a prolate~~ spheroid — the coefficient associated with the longest axis is,		When the length of the intermediate axis is the same as the length of the longest axis — that is, when we are dealing with an oblate spheroid — the coefficient associated with the longest axis is,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Tohline: /* The Case Where n = 1 */

2020-09-24T22:00:59Z

The Case Where n = 1

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	</td></tr>		</td></tr>
	</table>		</table>
	Applying this result to each of the other three definite integrals gives us,
			<span id="GravFor1">Applying this result to each of the other three definite integrals gives us,</span>
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

← Older revision		Revision as of 03:46, 11 December 2020
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	* [[User:Tohline/Apps/MaclaurinSpheroids#Maclaurin_Spheroids_.28axisymmetric_structure.29\|Properties of Maclaurin Spheroids]]		* [[User:Tohline/Apps/MaclaurinSpheroids#Maclaurin_Spheroids_.28axisymmetric_structure.29\|Properties of Maclaurin Spheroids]]
	* [[User:Tohline/Apps/MaclaurinSpheroids/GoogleBooks#Excerpts_from_A_Treatise_of_Fluxions\|Excerpts from Maclaurin's (1742) ''A Treatise of Fluxions'']]		* [[User:Tohline/Apps/MaclaurinSpheroids/GoogleBooks#Excerpts_from_A_Treatise_of_Fluxions\|Excerpts from Maclaurin's (1742) ''A Treatise of Fluxions'']]
			* [[User:Tohline/ThreeDimensionalConfigurations/FerrersPotential#Ferrers_.281877.29_Gravitational_Potential_for_Inhomogeneous_Ellipsoids\|Inhomogeneous Ellipsoids Leading to Ferrers Potentials]]

	=Footnotes=		=Footnotes=