ABSTRACT
Throughout this and the following chapters, orthogonal coordinate systems will be used. Figure 1.1 shows such a system, with base vectors e1, e2, and e3. The scalar product of vector analysis satisfies
ei·ej=δij (1.4)
The vector product satisfies
(1.5)
It is an obvious step to introduce the alternating operator, εijk, also known as the ijkth entry of the permutation tensor:
(1.6)
Consider two vectors, v and w. It is convenient to use two different types of notation. In tensor indicial notation, denoted by (*T), v and w are represented as
*T) v=viei w=wiei (1.7)
Occasionally, base vectors are not displayed, so that v is denoted by vi. By displaying base vectors, tensor indicial notation is explicit and minimizes confusion and ambiguity. However, it is also cumbersome.
