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Orthogonal Curvilinear Coordinates

Published online by Cambridge University Press:  03 November 2016

T. A. S. Jackson
T. A. S. Jackson*
Affiliation:
Dept. of Applied Mathematics, The University, Liverpool 3
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Extract

Although the gradient of a scalar, and the curl and divergence of a vector can be obtained by various elementary methods in terms of curvilinear components and coordinate vectors, the corresponding results for the components of strain and the vector divergence of stress are usually obtained by specializing the formulae for covariant derivatives. The purpose of this note is to give an elementary approach to these latter results in the spirit of the theory of Cartesian tensors. Apart from standard elementary vector analysis the only prerequisite is a geometrical appreciation of the analysis of deformation. For completeness an elementary analytical derivation of the results about gradient, curl and divergence is given first by a method which, whilst certainly not new, does not appear to be very well known.

Type
Research Article
Information
The Mathematical Gazette , Volume 50 , Issue 371 , February 1966 , pp. 28 - 30
Copyright
Copyright © Mathematical Association 1966

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