Appendix

A.1 Summary of Vector Notation

The following write‐up concerning vector and tensor notation is developed from the work of many authors but I like the compendium by Bird et al. [1] the most.

A.1.1 Unit Vectors

Unit vectors are vectors of unit length in each of three orthogonal directions. The unit vectors are . The following two properties summarize the dot and cross products of the unit vectors:

A.1-1

Figure A.1-1 shows the directional characteristics of the three unit vectors.

A.1.2 Definition of a Vector

A vector is a quantity that has a magnitude and a direction associated with it. The vector υ can be written as:

A.1-2

where are unit vectors oriented in the orthogonal directions and are component vectors oriented in the orthogonal directions. υ i are the component vector magnitudes.

If the vector is ...

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