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).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.
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).
Applications Polar plotters use two-center bipolar coordinates to describe the drawing paths required to draw a target image.
See also
Bipolar coordinates Biangular coordinates Lemniscate of Bernoulli Oval of Cassini Cartesian oval Ellipse
References