## Bipolar Cylindrical Coordinates

A set of Curvilinear Coordinates defined by

 (1) (2) (3)

where , , and . There are several notational conventions, and whereas is used in this work, Arfken (1970) prefers . The following identities show that curves of constant and are Circles in -space.
 (4)

 (5)

The Scale Factors are
 (6) (7) (8)

The Laplacian is
 (9)

Laplace's Equation is not separable in Bipolar Cylindrical Coordinates, but it is in 2-D Bipolar Coordinates.

References

Arfken, G. Bipolar Coordinates (, , ).'' §2.9 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 97-102, 1970.