Tensor theory is extremely useful in advanced engineering theory. It is used to help describe or model many natural phenomena such as: physical forces, potential fields, particle or control element motion, wave propagation, etc. In mathematics, a tensor is a certain kind of geometrical entity, or alternatively generalized quantity. The tensor concept includes the ideas of scalar, vector and linear operator. ... Engineering is the application of science to the needs of humanity. ... In physics, a potential is a scalar quantity that can be used to analyze the effects of complicated vectorial forces and similar quantities by means of simple conservation laws. ... A particle is In particle physics, a basic unit of matter or energy. ... A wave crashing against the shore A wave is a disturbance that propagates. ...

Constructions notes:

A^i'j'_k' = x^i'_i x^j'_j y^k_k' A^ij_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. Aerospace engineering is the branch of engineering concerning aircraft, spacecraft and related topics. ... In fluid dynamics, the Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes are a set of nonlinear partial differential equations that describe the flow of fluids such as liquids and gases. ... Vorticity is a mathematical concept used in fluid dynamics. ... -1... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Hydrodynamics is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. ...

See also

• Application of tensor theory in physics