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 curvesof constant 
and 
are Circles in 
-space. | (4) |
 | (5) |
 | |  | (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.
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