Application of tensor theory in engineering: Difference between revisions

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Revision as of 07:43, 25 October 2005

Tensors are frequently used in engineering to describe measured quantities.

Common applications

Measuring deformations (finite deformation tensors) and strain (strain tensor) in continuum mechanics
Representing diffusion as a tensor in Diffusion tensor imaging

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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]].
-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]] ([[strain tensor]]) in [[continuum mechanics]]
+* Representing [[diffusion]] as a tensor in [[Diffusion tensor imaging]]
-Specific examples are:
+== See also ==
-* [[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<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>.
-== See also ==
 * [[Application of tensor theory in physics]]
+* [[Mathematical physics]]
+* [[Tensor]]
 [[Category:Tensors]]
+[[Category:Engineering]]

wikademia>Karol Langner

Revision as of 07:43, 25 October 2005

Common applications

See also