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, and .[1] This system is very useful in some scientific applications (e.g. calculating the electric field of a dipole on a plane).[2][3]
- For related concepts, see Bipolar coordinates.
Two-center bipolar coordinates.
Transformation to Cartesian coordinates
The transformation to Cartesian coordinates from two-center bipolar coordinates is
where the centers of this coordinate system are at and .[1]
Transformation to polar coordinates
When x>0 the transformation to polar coordinates from two-center bipolar coordinates is
where is the distance between the poles (coordinate system centers).
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See also
- Biangular coordinates
- Lemniscate of Bernoulli
- Oval of Cassini
- Cartesian oval
- Ellipse
References
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