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[[Tensor]] theory is extremely useful in advanced engineering theory.  It is used to help describe or model many natural phenomenon such as: [[physical force]]s, [[potential field]]s, [[particle]] or [[control element]] motion, [[wave]] propagation, etc.
[[Tensor]]s are frequently used in [[engineering]] to describe measured [[physical quantity|quantities]].


Constructions notes:
== Common applications ==


:A<sup>i'</sup><sup>j'</sup><sub>k'</sub> = x<sup>i'</sup><sub>i</sub> x<sup>j'</sup><sub>j</sub> y<sup>k</sup><sub>k'</sub> A<sup>i</sup><sup>j</sup><sub>k</sub>
* Measuring [[deformation]]s ([[finite deformation tensors]]) and [[Strain (materials science)|strain]] ([[strain tensor]]) in [[continuum mechanics]]
* Representing [[diffusion]] as a tensor in [[diffusion tensor imaging]]


== See also ==


Specific examples are:
* [[Application of tensor theory in physics]]
* [[Mathematical physics]]
* [[Tensor]]


aeronautical engineering
[[Category:Tensors]]
 
{{ntnes}}
[[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<sub>r</sub>
 
::In the [[Lagrangian method]], all particles are then described by:
 
Equation (1)  z<sub>r</sub>=z<sub>r</sub>(a,t)  where a stands for the set of 3 labels representing the 3 dimensions or axis of Euclidean space ... x<sub>i</sub>,x<sub>j</sub>,x<sub>k</sub>.

Latest revision as of 08:05, 22 February 2011

Tensors are frequently used in engineering to describe measured quantities.

Common applications

See also

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