Two-center bipolar coordinates

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
For related concepts, see Bipolar coordinates.
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]

Transformation to Cartesian coordinates[edit]

Cartesian coordinates and polar 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[edit]

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[edit]

References[edit]