Two-center bipolar coordinates
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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]
Transformation to Cartesian coordinates
When the centers are at and , the transformation to Cartesian coordinates from two-center bipolar coordinates is
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).
See also
- Bipolar coordinates
- Biangular coordinates
- Lemniscate of Bernoulli
- Oval of Cassini
- Cartesian oval
- Ellipse
References