User:Tohline/Appendix/Mathematics/ScaleFactors
Scale Factors for Orthogonal Curvilinear Coordinate Systems
Here we lean heavily on the class notes and associated references that have been provided by P. A. Kelly in a collection titled, Mechanics Lecture Notes: An Introduction to Solid Mechanics, as they appeared online in early 2021. See especially the subsection of Part III in which the properties of Vectors and Tensors are discussed.
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Getting Started
Following Kelly, we will use <math>~\hat{e}_i</math> and <math>~x_i</math> when referencing, respectively, the three (i = 1,3) basis vectors and coordinate "curves" of the Cartesian coordinate system; and we will use <math>~\hat{g}_i</math> and <math>~\Theta_i</math> when referencing, respectively, the three (i = 1,3) basis vectors and coordinate curves of some other, curvilinear coordinate system.
See Also
- Tohline, J. E., (2008) Computing in Science & Engineering, vol. 10, no. 4, pp. 84-85 — Where is My Digital Holographic Display? [ PDF ]
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