Toroidal Coordinates
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 aredefined 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 ( Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 666, 1953., , ).'' §2.13 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 112-115, 1970.
- Primitive Root of Unity
- Primitive Semiperfect Number
- Primitive Sequence
- Primorial
- Prince Rupert's Cube
- Principal
- Principal Curvatures
- Principal Curve
- Principal Direction
- Principal Ideal
- Principal Normal Vector
- Principal Quintic Form
- Principal Radius of Curvature
- Principal Value
- Principal Vector
- Principal Vertex
- Principle
- Pringsheim's Theorem
- Printer's Errors
- Prior Distribution
- Prism
- Prismatic Ring
- Prismatoid
- Prismoid
- Prisoner's Dilemma