https://ideawaza.com/api.php?action=feedcontributions&feedformat=atom&user=80.168.224.126IdeaWazaWiki - User contributions [en]2026-09-29T05:15:30ZUser contributionsMediaWiki 1.46.0https://ideawaza.com/index.php?title=Application_of_tensor_theory_in_engineering&diff=11309Application of tensor theory in engineering2005-06-28T17:31:18Z<p>80.168.224.126: * Application of tensor theory in physics</p>
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<div>'''[[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.<br />
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Constructions notes:<br />
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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><br />
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Specific examples are:<br />
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* [[Aeronautical engineering]]<br />
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* [[Navier-Stokes equations]] Presented in partial differential equation form.<br />
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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.<br />
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* [[Continuum mechanics]]<br />
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* dynamics of systems of rigid (assumed incompressible) bodies and particles<br />
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* stress and strain within elastic bodies <br />
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* [[electromagnetism]] [[Maxwell's Equations]]<br />
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* [[Hydrodynamics]]<br />
:Tensor equations to model fluid flow can be derived as follows:<br />
::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.<br />
::We shall use rectangular cartesian coordinates to describe our Euclidean 3 space .... z<sub>r</sub><br />
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::In the [[Lagrangian method]], all particles are then described by:<br />
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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>.<br />
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== See also ==<br />
* [[Application of tensor theory in physics]]<br />
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[[Category:Tensors]]</div>80.168.224.126