A system of Curvilinear Coordinates for which several different notations are commonly used. In this work
(, , ) is used, whereas Arfken (1970) uses (, , ). The toroidal coordinates are
defined by

(1) | |||

(2) | |||

(3) |

where is the Hyperbolic Sine and is the Hyperbolic Cosine. The Scale Factors are

(4) | |||

(5) | |||

(6) |

The Laplacian is

(7) | |

(8) |

**References**

Arfken, G. ``Toroidal Coordinates (, , ).'' §2.13 in
*Mathematical Methods for Physicists, 2nd ed.* Orlando, FL: Academic Press, pp. 112-115, 1970.

Morse, P. M. and Feshbach, H. *Methods of Theoretical Physics, Part I.* New York: McGraw-Hill, p. 666, 1953.

© 1996-9

1999-05-26