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GENERAL INFORMATION
appendix D, Coordinate Expansions of Vector Differential Operators
Published: 04 November 2004
Chapter DOI: http://dx.doi.org/10.1117/3.581869.apd
Chapter Page Count: 10
pages
Table of Contents
- 1. Introduction
Chapter Contents
- D.1 Cartesian Coordinate Expansions
- D.1.1 Cartesian coordinate expansions of vector differential operators
- (a) The divergence of vector and dyadic fields
- (b) The curl of vector and dyadic fields
- (c) The gradient of scalar, vector, and dyadic fields
- D.1.2 Cartesian coordinate expansions of second-order vector differential operators
- (a) The scalar and vector Laplacian
- (b) The curl of the curl of a vector field
- (c) The gradient of the divergence
- D.2 Cylindrical Coordinate Expansions
- D.2.1 Cylindrical coordinate expansions of first-order vector differential operators
- (a) The divergence of vector and dyadic fields
- (b) The curl of vector and dyadic fields
- (c) The gradient of scalar, vector, and dyadic fields
- D.2.2 Cylindrical coordinate expansions of second-order vector differential operators
- (a) The scalar and vector Laplacian
- (b) The curl of the curl of a vector field
- (c) The gradient of the divergence
Excerpt
This appendix provides Cartesian and cylindrical coordinate expansions of first- and second-order vector differential operators acting on scalar, vector, and dyadic operands. The divergence and curl of vector and dyadic fields and the gradient of scalar, vector, and dyadic fields are provided with applications cited for the curl of the strain dyadic and the gradient of the stress dyadic. In addition the scalar and vector Laplacian expansions are listed.
©2005 Society of Photo-Optical Instrumentation Engineers
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