Algebraic function - Revision history

en>Waldir: /* See also */ +1

2014-09-16T18:31:49Z

See also: +1

← Older revision		Revision as of 20:31, 16 September 2014
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en>ClueBot NG: Reverting possible vandalism by 162.78.70.120 to version by D.Lazard. False positive? Report it. Thanks, ClueBot NG. (1718004) (Bot)

2014-02-25T20:40:52Z

Reverting possible vandalism by 162.78.70.120 to version by D.Lazard. False positive? Report it. Thanks, ClueBot NG. (1718004) (Bot)

← Older revision		Revision as of 22:40, 25 February 2014
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	~~In [[celestial mechanics]],~~ the ~~'''eccentricity vector''' of~~ a ~~[[Kepler orbit]] is the [[vector (geometric)\|vector]] that points towards the [[periapsis]]~~ and has ~~a magnitude equal to the orbit's scalar [[orbital eccentricity\|eccentricity]]~~. The ~~magnitude~~ is ~~[[unitless]]. For Kepler orbits the~~ '~~''eccentricity vector''' is a constant of motion~~. ~~Its main use is~~ in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the [[Osculating orbit\|osculating]] eccentricity vector to change continuously. For the eccentricity and ~~[[argument of periapsis]] parameters, eccentricity zero (circular orbit) corresponds to a singularity~~.		The title of the writer is Nestor. His working day job is a cashier and his wage has been truly satisfying. The preferred pastime for my kids and me is playing crochet and now I'm trying to earn cash with it. He presently lives in Arizona and his mothers and fathers live nearby.<br><br>My web-site: [http://Www.Monsterpest.com/UserProfile/tabid/343/userId/22217/Default.aspx monsterpest.com]

	~~==Calculation==~~
	~~The '''eccentricity vector'''~~ <~~math~~> ~~\mathbf{e} \,~~<~~/math~~> ~~can be calculated<ref>{{cite book \|title=The Kepler Problem \|first=Bruno \|last=Cordani \|page=22 \|location= \|publisher=Birkhaeuser \|year=2003 \|isbn=3~~-~~7643-6902-7 }}<~~/~~ref>~~

	~~:<math> \mathbf{e} = {\mathbf{v}\times\mathbf{h}\over{\mu}} - {\mathbf{r}\over{\left\|\mathbf{r}\right\|}}<~~/~~math>~~
	~~where:~~
	*<math> \mathbf{v}\,\!</~~math> is [[velocity vector]]~~
	*<math>\mathbf{h}\,\!</~~math> is [[Specific relative angular momentum\|specific angular momentum vector]] (equal to <math>\mathbf{r}\times\mathbf{v}<~~/~~math>)~~
	*<math>\mathbf{r}\,\!</~~math> is [[position vector]]~~
	*<math>\mu\,\!</~~math> is [[standard gravitational parameter]]~~

	~~or equivalently:~~
	~~:<math> \mathbf{e} = {\mathbf{\left \|v \right \|}^2 \mathbf{r} \over {\mu}} - {(\mathbf{r} \cdot \mathbf{v} ) \mathbf{v} \over{\mu}} - {\mathbf{r}\over{\left\|\mathbf{r}\right\|}}<~~/~~math>~~

	~~==See also==~~
	*[[Kepler orbit]]
	*[[Orbit]]
	*[[Eccentricity (orbit)\|Eccentricity]]
	*[[Laplace–Runge–Lenz vector]]

	~~==References==~~
	~~{{Reflist}}~~

	~~{{DEFAULTSORT:Eccentricity Vector}}~~
	~~[[Category:Orbits]]~~
	~~[[Category:Vectors]~~]

en>D.Lazard: Rm WP:OR wrong assertion: implicit function theorem suffices to understand the concept

2014-01-21T17:50:47Z

Rm WP:OR wrong assertion: implicit function theorem suffices to understand the concept

← Older revision		Revision as of 19:50, 21 January 2014
Line 1:		Line 1:
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			==Calculation==
			The '''eccentricity vector''' <math> \mathbf{e} \,</math> can be calculated<ref>{{cite book \|title=The Kepler Problem \|first=Bruno \|last=Cordani \|page=22 \|location= \|publisher=Birkhaeuser \|year=2003 \|isbn=3-7643-6902-7 }}</ref>

			:<math> \mathbf{e} = {\mathbf{v}\times\mathbf{h}\over{\mu}} - {\mathbf{r}\over{\left\|\mathbf{r}\right\|}}</math>
			where:
			*<math> \mathbf{v}\,\!</math> is [[velocity vector]]
			*<math>\mathbf{h}\,\!</math> is [[Specific relative angular momentum\|specific angular momentum vector]] (equal to <math>\mathbf{r}\times\mathbf{v}</math>)
			*<math>\mathbf{r}\,\!</math> is [[position vector]]
			*<math>\mu\,\!</math> is [[standard gravitational parameter]]

			or equivalently:
			:<math> \mathbf{e} = {\mathbf{\left \|v \right \|}^2 \mathbf{r} \over {\mu}} - {(\mathbf{r} \cdot \mathbf{v} ) \mathbf{v} \over{\mu}} - {\mathbf{r}\over{\left\|\mathbf{r}\right\|}}</math>

			==See also==
			*[[Kepler orbit]]
			*[[Orbit]]
			*[[Eccentricity (orbit)\|Eccentricity]]
			*[[Laplace–Runge–Lenz vector]]

			==References==
			{{Reflist}}

			{{DEFAULTSORT:Eccentricity Vector}}
			[[Category:Orbits]]
			[[Category:Vectors]]

en>Jp.martin-flatin: Added links and categories

2012-08-22T15:49:36Z

Added links and categories

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