Two-center bipolar coordinates
- For related concepts, see Bipolar coordinates.
In mathematics, two-center bipolar coordinates is a coordinate system, based on two coordinates which give distances from two fixed centers, and . This system is very useful in some scientific applications (e.g. calculating the electric field of a dipole on a plane).
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 .
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).
- Weisstein, Eric W. "Bipolar coordinates". MathWorld.
- R. Price, The Periodic Standing Wave Approximation: Adapted coordinates and spectral methods.
- The periodic standing-wave approximation: nonlinear scalar fields, adapted coordinates, and the eigenspectral method.
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