CaltechAUTHORS
  A Caltech Library Service

Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates

Lewis, H. Ralph and Bellan, Paul M. (1990) Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates. Journal of Mathematical Physics, 31 (11). pp. 2592-2596. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20120509-111024688

[img]
Preview
PDF - Published Version
See Usage Policy.

351Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20120509-111024688

Abstract

It is demonstrated that (i) the postulate of infinite differentiability in Cartesian coordinates and (ii) the physical assumption of regularity on the axis of a cylindrical coordinate system provide significant simplifying constraints on the coefficients of Fourier expansions in cylindrical coordinates. These constraints are independent of any governing equations. The simplification can provide considerable practical benefit for the analysis (especially numerical) of actual physical problems. Of equal importance, these constraints demonstrate that if A is any arbitrary physical vector, then the only finite Fourier terms of A_r and A_θ are those with m=1 symmetry. In the Appendix, it is further shown that postulate (i) may be inferred from a more primitive assumption, namely, the arbitrariness of the location of the cylindrical axis of the coordinate system.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.529009DOIUNSPECIFIED
http://jmp.aip.org/resource/1/jmapaq/v31/i11/p2592_s1PublisherUNSPECIFIED
Additional Information:© 1990 American Institute of Physics. Received 12 March 1990; accepted for publication 20 June 1990. The authors are indebted to J. L. Schwarzmeier, R. A. Nebel, and M. A. Schalit for many stimulating conversations. This work was supported by the U.S. Department of Energy.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:FOURIER ANALYSIS, CARTESIAN COORDINATES, SYMMETRY, BOUNDARY CONDITIONS, COORDINATES, DIFFERENTIAL EQUATIONS, TRANSFORMATIONS, SINGULARITY, MAGNETOHYDRODYNAMICS
Classification Code:PACS: 02.70.-c; 52.30.-q
Record Number:CaltechAUTHORS:20120509-111024688
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120509-111024688
Official Citation: Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates H. Ralph Lewis and Paul M. Bellan J. Math. Phys. 31, 2592 (1990); http://dx.doi.org/10.1063/1.529009
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31377
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 May 2012 19:56
Last Modified:26 Dec 2012 15:10

Repository Staff Only: item control page