Next: Tensors and Tensor Notation
Up: Cartesian Tensors
Previous: Cartesian Tensors
As we saw in Appendix A, many physical entities can be represented mathematically as
either scalars or
vectors, depending on their transformation properties under rotation of the coordinate axes.
However, it turns out that scalars and vectors are particular types of a more general class of
mathematical constructs known as tensors. In fact, a scalar is a tensor of order zero, and a vector is a tensor of
order one. In fluid mechanics, certain important physical entities (i.e., stress and rate of strain) are represented mathematically
by tensors of order greater than one. It is therefore necessary to supplement our investigation of fluid mechanics with a brief discussion of the mathematics
of tensors. For the sake of simplicity, we shall limit this discussion to Cartesian coordinate systems. Tensors expressed
in such coordinate systems are known as Cartesian tensors. For more information on Cartesian tensors see
Jeffries 1961, Riley 1974, and Temple 2004.