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| '''[[Tensor]] theory''' is extremely useful in advanced [[engineering]] theory. It is used to help describe or model many natural phenomena 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]]. |
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| Constructions notes:
| | == Common applications == |
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| :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]] |
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| | == See also == |
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| Specific examples are:
| | * [[Application of tensor theory in physics]] |
| | * [[Mathematical physics]] |
| | * [[Tensor]] |
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| * [[Aeronautical engineering]]
| | [[Category:Tensors]] |
| | | {{ntnes}} |
| * [[Navier-Stokes equations]] Presented in partial differential equation form.
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| * [[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.
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| * [[Continuum mechanics]]
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| * dynamics of systems of rigid (assumed incompressible) bodies and particles
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| * stress and strain within elastic bodies
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| * [[electromagnetism]] [[Maxwell's Equations]]
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| * [[Hydrodynamics]]
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| :Tensor equations to model fluid flow can be derived as follows:
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| ::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.
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| ::We shall use rectangular cartesian coordinates to describe our Euclidean 3 space .... z<sub>r</sub>
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| ::In the [[Lagrangian method]], all particles are then described by:
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| 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>.
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Tensors are frequently used in engineering to describe measured quantities.
Common applications
See also
