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Application of tensor theory in engineering science

Tensor theory is extremely useful in advanced engineering theory. It is used to help describe or model many natural phenomenon such as: physical forces, potential fields, particle or control element motion, wave propagation, etc.

Constructions notes:

Ai'j'k' = xi'i xj'j ykk' Aijk

Specific examples are:

Tensor equations to model fluid flow can be derived as follows:
Assume the fluid consists of particles which can be individually tracked as they move in relation to Euclidean 3-space. Thus an individual particle can be tracked as it moves.
We shall use rectangular cartesian coordinates to describe our Euclidean 3 space .... zr

In the Lagrangian method, all particles are then described by:

Equation (1) zr=zr(a,t) where a stands for the set of 3 labels representing the 3 dimensions or axis of Euclidean space ... xi,xj,xk.