Oblate Spheroidal Coordinates
A system of Curvilinear Coordinates in which two sets of coordinate surfaces are obtained by revolving the curves ofthe Elliptic Cylindrical Coordinates about the y-Axis which is relabeled the z-Axis. The third setof coordinates consists of planes passing through this axis.
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
where
, 
, and 
. Arfken (1970) uses 
instead of 
. The Scale Factors are | |  | (4) |
 | | | (5) |
 | |  | (6) |
The Laplacian is
 | |
 | |
 | |
 | |
 | |
 | (7) |
 | (8) |
An alternate form useful for ``two-center'' problems is defined by
 | |  | (9) |
 | |  | (10) |
 | |  | (11) |
 | |  | (12) |
where
, 
, and 
. In thesecoordinates, | |  | (13) |
| |  | (14) |
| |  | (15) |
(Abramowitz and Stegun 1972). The Scale Factors are
 | |  | (16) |
 | |  | (17) |
 | |  | (18) |
and the Laplacian is
 | (19) |
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Definition of Oblate Spheroidal Coordinates.'' §21.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 752, 1972. Arfken, G. ``Prolate Spheroidal Coordinates ( Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 663, 1953.
, 
, 
).'' §2.11 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 107-109, 1970.
- Attractor
- Auction
- Augend
- Augmented Amicable Pair
- Augmented Dodecahedron
- Augmented Hexagonal Prism
- Augmented Pentagonal Prism
- Augmented Polyhedron
- Augmented Sphenocorona
- Augmented Triangular Prism
- Augmented Tridiminished Icosahedron
- Augmented Truncated Cube
- Augmented Truncated Dodecahedron
- Augmented Truncated Tetrahedron
- Aureum Theorema
- Aurifeuillean Factorization
- Ausdehnungslehre
- Authalic Latitude
- Autocorrelation
- Automorphic Function
- Automorphic Number
- Automorphism
- Automorphism Group
- Autonomous
- Autoregressive Model