List of operators - Revision history

en>Colonies Chris: sp, date & link fixes; unlinking common words, replaced: Fubini-Study → Fubini–Study using AWB

2014-03-13T18:01:03Z

sp, date & link fixes; unlinking common words, replaced: Fubini-Study → Fubini–Study using AWB

← Older revision		Revision as of 20:01, 13 March 2014
Line 1:		Line 1:
	~~{{distinguish\|bipolar coordinates}}~~		The writer is called Araceli Gulledge. I am a production and distribution officer. The thing I adore most flower arranging and now I have time to consider on new issues. Delaware has usually been my residing location and will never transfer.<br><br>Also visit my weblog - extended auto warranty ([http://Www.Gahaghan.com/UserProfile/tabid/42/userId/44115/Default.aspx mouse click the following internet site])

	~~[[Image:Two-centerBipolarCoordinateSystem.JPG\|right\|frame\|Two-center bipolar coordinates~~.]]

	~~In [[mathematics]], '''two-center bipolar coordinates''' is~~ a ~~coordinate system, based on two coordinates which give distances from two fixed centers, <math>c_1</math>~~ and ~~<math>c_2</math>~~.<ref name=bip>{{mathworld\|urlname=BipolarCoordinates\|title=Bipolar coordinates}}</ref> This system is very useful in some {{which\|date=May 2013}} scientific applications.<ref>[http://www.physics.utah.edu/~rprice/AREA51DOCS/paperIIa.pdf R. ~~Price, The Periodic Standing Wave Approximation: Adapted coordinates~~ and ~~spectral methods~~.]<~~/ref~~><~~ref~~>[http://~~arxiv~~.~~org/abs/gr-qc/0502034v1 The periodic standing-wave approximation: nonlinear scalar fields, adapted coordinates, and the eigenspectral method~~.]</~~ref>~~

	~~==Cartesian coordinates==~~
	~~[[Image:Polar to cartesian.svg\|thumb\|right\|350px\|Cartesian coordinates and polar coordinates.]]~~
	~~The transformation to Cartesian coordinates <math>(x,\ y)<~~/~~math> from two-center bipolar coordinates <math>(r_1,\ r_2)<~~/~~math> is~~
	~~:<math>~~
	~~x = \frac{r_1^2-r_2^2}{4a}~~
	</~~math>~~

	~~:<math>~~
	~~y = \pm \frac{1}{4a}\sqrt{16a^2r_1^2-(r_1^2-r_2^2+4a^2)^2}~~
	~~</math>~~
	~~where the centers of this coordinate system are at <math>(+a,\ 0)<~~/~~math> and <math>(-a,\ 0)<~~/~~math>~~.~~<ref name=bip />~~

	~~==Polar coordinates==~~
	~~The transformation to polar coordinates from two-center bipolar coordinates is~~
	~~:<math>~~
	~~r = \sqrt{\frac{r_1^2+r_2^2-2a^2}{2}}~~
	~~</math>~~

	~~:<math>\theta = \arctan \left( \frac{\sqrt{8a^2(r_1^2+r_2^2 - 2a^2)-(r_1^2 - r_2^2)^2}}{r_1^2 - r_2^2}\right)\,\!</math>~~
	~~where <math>2 a</math> is~~ the ~~distance between the poles (coordinate system centers~~).

	~~==See also==~~
	*[[Biangular coordinates]]

	~~==References==~~
	~~<references/>~~

	~~{{Orthogonal coordinate systems}}~~

	~~[[Category:Coordinate systems\|Two-center bipolar coordinates]]~~


	~~{{geometry-stub}}~~

en>Ozob: Remove obscure, non-standard operators again

2013-05-02T01:15:24Z

Remove obscure, non-standard operators again

← Older revision		Revision as of 03:15, 2 May 2013
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	~~Hi there~~, ~~I am Felicidad Oquendo. Meter studying~~ is ~~exactly where my primary earnings arrives~~ from ~~but soon I'll be on my own~~. ~~Arizona~~ is ~~her beginning place~~ and ~~she will by no means transfer. Climbing is what love performing~~.<br><br>~~Take a look at my blog post~~ [http://~~Freebusinesscollege~~.~~com~~//~~read_blog~~/~~198199~~/~~great~~-~~ideas~~-~~about~~-~~auto~~-~~repair~~-~~that~~-~~anyone~~-~~can~~-~~use cars warranty~~]		{{distinguish\|bipolar coordinates}}

			[[Image:Two-centerBipolarCoordinateSystem.JPG\|right\|frame\|Two-center bipolar coordinates.]]

			In [[mathematics]], '''two-center bipolar coordinates''' is a coordinate system, based on two coordinates which give distances from two fixed centers, <math>c_1</math> and <math>c_2</math>.<ref name=bip>{{mathworld\|urlname=BipolarCoordinates\|title=Bipolar coordinates}}</ref> This system is very useful in some {{which\|date=May 2013}} scientific applications.<ref>[http://www.physics.utah.edu/~rprice/AREA51DOCS/paperIIa.pdf R. Price, The Periodic Standing Wave Approximation: Adapted coordinates and spectral methods.]</ref><ref>[http://arxiv.org/abs/gr-qc/0502034v1 The periodic standing-wave approximation: nonlinear scalar fields, adapted coordinates, and the eigenspectral method.]</ref>

			==Cartesian coordinates==
			[[Image:Polar to cartesian.svg\|thumb\|right\|350px\|Cartesian coordinates and polar coordinates.]]
			The transformation to Cartesian coordinates <math>(x,\ y)</math> from two-center bipolar coordinates <math>(r_1,\ r_2)</math> is
			:<math>
			x = \frac{r_1^2-r_2^2}{4a}
			</math>

			:<math>
			y = \pm \frac{1}{4a}\sqrt{16a^2r_1^2-(r_1^2-r_2^2+4a^2)^2}
			</math>
			where the centers of this coordinate system are at <math>(+a,\ 0)</math> and <math>(-a,\ 0)</math>.<ref name=bip />

			==Polar coordinates==
			The transformation to polar coordinates from two-center bipolar coordinates is
			:<math>
			r = \sqrt{\frac{r_1^2+r_2^2-2a^2}{2}}
			</math>

			:<math>\theta = \arctan \left( \frac{\sqrt{8a^2(r_1^2+r_2^2 - 2a^2)-(r_1^2 - r_2^2)^2}}{r_1^2 - r_2^2}\right)\,\!</math>
			where <math>2 a</math> is the distance between the poles (coordinate system centers).

			==See also==
			*[[Biangular coordinates]]

			==References==
			<references/>

			{{Orthogonal coordinate systems}}

			[[Category:Coordinate systems\|Two-center bipolar coordinates]]


			{{geometry-stub}}

en>Favonian: Disambiguated: Borel transform → Borel summation using Dab solver

2011-11-16T19:46:56Z

Disambiguated: Borel transform → Borel summation using Dab solver

New page

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