Separability in a class of coordinate systems

✍ Scribed by Parry Moon; Domina Eberle Spencer

• Publisher: Elsevier Science
• Year: 1952
• Tongue: English
• Weight: 626 KB
• Volume: 254
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(52)90460-2

✦ Synopsis

A study is made of separability conditions for the Helmholtz and Laplace equations. Attention is confined to the most useful case for physical applications; namely, (a) The coordinate system is either cylindrical or it has rotational symmetry, and (b) The potential is independent of the third space variable.

Necessary and sufficient conditions are tabulated, by which one can easily determine if a proposed coordinate system will allow solutions by the method of separation of variables.

(a) Cylindrical Systems. The coordinate surfaces consist of a family of parallel planes and two families of cylinders, the generators of