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) |

(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.

© 1996-9

1999-05-26