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- 426 bytes (64 words) - 04:13, 17 July 2015
- ...cal physics that can be thought of as a generalization of a vector. While tensors can be defined in a purely mathematical sense, they are most useful in conn ...ining contravariant or mixed tensors, but not in defining purely covariant tensors, so this definition is not circular.</ref>. If a form <math>\Phi\,</math> ...9 KB (1,509 words) - 11:57, 5 November 2020
- == Tensors in Solid Mechanics == ...rannon/public/Tensors.pdf monograph by R. M. Brannon]. An introduction to tensors in continuum mechanics can be found in ''An Introduction to Continuum Mecha ...51 KB (7,338 words) - 02:38, 5 October 2021
- :::::''This article presumes that the reader has read [[Tensors/Bases, components, and dual spaces]]''. ...index notation, thereby giving the reader a feeling for the power of using tensors. ...11 KB (1,936 words) - 15:57, 25 February 2018
- :::::''This article presumes that the reader has read [[Tensors/Definitions]]''. ...he space of linear, real-valued, functions of linear forms. Recall from [[Tensors/Definitions|Definitions]] that another name for a linear, real-valued, func ...9 KB (1,508 words) - 15:56, 25 February 2018
- ...at the reader has read the earlier articles in the series, starting with [[Tensors/Definitions]]''. ...nts of a given vector change when the basis changes, the components of all tensors must change in order to make the formulas get the same answers. How do the ...6 KB (1,003 words) - 16:55, 12 January 2024
- ...l{V}</math>.<ref>http://en.wikiversity.org/wiki/Introduction_to_Elasticity/Tensors</ref> Thus, we can write ==Vectors: 1<sup>st</sup> order tensors== ...25 KB (3,939 words) - 21:25, 6 March 2022
- ...couraged to read more from the references. Due to this short introduction, Tensors will not be used as a separate chapter. ...l{V}</math>.<ref>http://en.wikiversity.org/wiki/Introduction_to_Elasticity/Tensors</ref> Thus, we can write: ...25 KB (3,962 words) - 05:20, 10 October 2024
- 20 KB (2,789 words) - 03:06, 7 September 2011
- ...ently being used as a sandbox for '' [[User:Guy vandegrift/Introduction to tensors in physics]]'''''</big> ...in physics/1|Preliminary drafts for STRAIN at '''Physics/A/Introduction to tensors in physics/1''']] ...15 KB (2,275 words) - 00:24, 23 April 2024
Page text matches
- ...at the reader has read the earlier articles in the series, starting with [[Tensors/Definitions]]''. ...nts of a given vector change when the basis changes, the components of all tensors must change in order to make the formulas get the same answers. How do the ...6 KB (1,003 words) - 16:55, 12 January 2024
- and strain tensors or the mechanical properties of a material. ...on if it transforms according to the transformation rules for second order tensors.''' ...6 KB (1,029 words) - 14:32, 20 December 2021
- ...of physical quantities within tensors. This is worth repeating: we can use tensors to write physical equations independent of the choice of coordinate [[../Si ...3 KB (396 words) - 03:48, 13 September 2020
- ...>\boldsymbol{A}</math> and <math>\boldsymbol{B}</math> be two second order tensors. Show that ...>\boldsymbol{A}</math> and <math>\boldsymbol{B}</math> be two second order tensors and let <math>\mathbf{a}</math> and <math>\mathbf{b}</math> ...4 KB (651 words) - 22:26, 25 July 2017
- ...tions|General Relativity]], and is the most powerful way to do vectors and tensors. ...ex notation]] • [[Tensors/Transformation rule under a change of basis|Tensors/Transformation rule under a change of basis]]'' ...6 KB (897 words) - 18:11, 14 October 2024
- :::::''This article presumes that the reader has read [[Tensors/Definitions]]''. ...he space of linear, real-valued, functions of linear forms. Recall from [[Tensors/Definitions|Definitions]] that another name for a linear, real-valued, func ...9 KB (1,508 words) - 15:56, 25 February 2018
- Several examples of tensors are [[../Velocity/|velocity]] [[../Vectors/|vector]], base vectors, [[../Me ...] for physics, engineering, and applied mathematics can also be written as tensors. Examples of differential equations that can be written in tensor form are ...12 KB (1,805 words) - 03:12, 13 September 2020
- ===Spectral decompositions of stretch tensors=== Hence the spectral decompositions of these strain tensors are ...6 KB (952 words) - 14:49, 4 October 2018
- ===Property Tensors=== ...2 KB (234 words) - 17:56, 6 September 2015
- ...cal physics that can be thought of as a generalization of a vector. While tensors can be defined in a purely mathematical sense, they are most useful in conn ...ining contravariant or mixed tensors, but not in defining purely covariant tensors, so this definition is not circular.</ref>. If a form <math>\Phi\,</math> ...9 KB (1,509 words) - 11:57, 5 November 2020
- Derive the transformation rule for second order tensors which is the transformation rule for second order tensors. ...3 KB (512 words) - 02:38, 5 October 2021
- :::::''This article presumes that the reader has read [[Tensors/Bases, components, and dual spaces]]''. ...index notation, thereby giving the reader a feeling for the power of using tensors. ...11 KB (1,936 words) - 15:57, 25 February 2018
- ...epends on the type of tensor and the nature of the rotation. For symmetric tensors, it's helpful to consider how the eigenvalues transform under orthogonal tr In summary, for symmetric tensors, eigenvalues are invariant under orthogonal transformations such as rotatio ...3 KB (430 words) - 07:52, 16 February 2024
- ====See [[Tensors]] for application to the mathematics of general relativity==== *See also '''[[Tensors]]''' ...5 KB (789 words) - 16:03, 13 June 2014
- ...l energy|energy]] '''W''' is a linear combination of two [[w:Invariants of tensors|invariants]] of the [[w:Finger tensor]] <math>\mathbf{B}</math>: ...<math>\overline{I}_2</math> are the first and the second [[w:Invariants of tensors|invariant]] of [[w:deviatoric]] component of the [[w:Finger tensor]]:<ref>T ...3 KB (408 words) - 22:32, 25 July 2017
- ...{I}}</math> is the fourth-order symmetric identity tensor.The two identity tensors are defined as ==Problem 2: Rotating Vectors and Tensors == ...5 KB (779 words) - 01:13, 26 July 2017
- Let A and B be tensors. Then ...1 KB (226 words) - 07:28, 22 August 2023
- ...tra stresses due to deformation are proportional to [[w:Finite deformation tensors|Finger tensor]]: ...B})</math> is the [[w:trace (linear algebra)|trace]] (or [[w:Invariants of tensors|first invariant]]) of [[w:Finger tensor]] <math>\mathbf {B} </math>. ...4 KB (608 words) - 22:32, 25 July 2017
- Now the strain and rotation tensors are given by ...2 KB (270 words) - 22:26, 25 July 2017
- ...[[w:stress (physics)|converted]] into any of the other conventional stress tensors, such as the [[w:Cauchy_stress_tensor|Cauchy Stress tensor]] which is given ...2 KB (273 words) - 22:32, 25 July 2017