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Online ISSN 1552-4485; Print ISSN 0033-569X
Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems
Author:
Vaughan H. Weston
Journal:
Quart. Appl. Math. 15 (1958), 420-427
MSC:
Primary 35.00
DOI:
https://doi.org/10.1090/qam/98238
MathSciNet review:
98238
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Abstract | References | Similar Articles | Additional Information
Abstract: In cylindrical and rotational coordinate systems, one of the variables can be separated out of the Helmholtz equation, leaving a second order partial differential equation in two variables. For a class of the coordinate systems, this equation is reducible to a recurrence set of ordinary differential equations in one variable, which are solvable by ordinary methods.
- Luther Pfahler Eisenhart, Separable systems of Stackel, Ann. of Math. (2) 35 (1934), no. 2, 284–305. MR 1503163, DOI https://doi.org/10.2307/1968433
- Parry Moon and Domina Eberle Spencer, Separability in a class of coordinate systems, J. Franklin Inst. 254 (1952), 227–242. MR 49438, DOI https://doi.org/10.1016/0016-0032%2852%2990460-2 V. Weston, Solutions of the toroidal wave equation and their applications, Ph.D. thesis, Univ. of Toronto. 1956
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Article copyright:
© Copyright 1958
American Mathematical Society