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:
- A^{i'}^{j'}_{k'} = x^{i'}_{i} x^{j'}_{j} y^{k}_{k'} A^{i}^{j}_{k}
Specific examples are:
aeronautical engineering
Navier-Stokes equations Presented in partial differential equation form.
Vorticity is an important quantity in various research, modeling and design calculations regarding lift, drag, and propulsion. It is a tensor quantity defined as: insert gif here when available.
Continuum mechanics
dynamics of systems of rigid (assumed incompressible) bodies and particles
stress and strain within elastic bodies
electromagnetism Maxwell's Equations
Hydrodynamics
- 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 .... z_{r}
- In the Lagrangian method[?], all particles are then described by:
Equation (1) z_{r}=z_{r}(a,t) where a stands for the set of 3 labels representing the 3 dimensions or axis of Euclidean space ... x_{i},x_{j},x_{k}.
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