A set of Curvilinear Coordinates defined by
. 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.
The Scale Factors are
The Laplacian is
Laplace's Equation is not separable in Bipolar Cylindrical Coordinates, but it is in 2-D Bipolar Coordinates.
Arfken, G. ``Bipolar Coordinates (, , ).'' §2.9 in
Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 97-102, 1970.
© 1996-9 Eric W. Weisstein