Two-center bipolar coordinates: Difference between revisions
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:<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> |
:<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> |
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where <math>2 a</math> |
where <math>2 a</math> is the distance between the poles (coordinate system centers). |
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==See also== |
==See also== |
Revision as of 20:02, 11 December 2013
In mathematics, two-center bipolar coordinates is a coordinate system, based on two coordinates which give distances from two fixed centers, and .[1] This system is very useful in some [which?] scientific applications.[2][3]
Cartesian coordinates
![](http://upload.wikimedia.org/wikipedia/commons/thumb/7/78/Polar_to_cartesian.svg/350px-Polar_to_cartesian.svg.png)
The transformation to Cartesian coordinates from two-center bipolar coordinates is
where the centers of this coordinate system are at and .[1]
Polar coordinates
The transformation to polar coordinates from two-center bipolar coordinates is
where is the distance between the poles (coordinate system centers).
See also
References