nach oben

Erschienen in:

2020 | OriginalPaper | Buchkapitel

9. Transversality and Skew Symmetric Properties

verfasst von : Manuel Laso, Nieves Jimeno

Erschienen in: Representation Surfaces for Physical Properties of Materials

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The reader may have wondered why almost only RS corresponding to projections such as \(:\underline{n}\,\underline{n}\,\),

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-40870-1_9/439456_1_En_9_IEq2_HTML.gif

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-40870-1_9/439456_1_En_9_IEq3_HTML.gif

have appeared up to now. As a matter of fact, we have also encountered projections along more than one direction: the calculation of the angular dependence of the shear modulus G (8.22) of a 2D fabric involved the use of two vectors (8.18). The calculation of polycrystalline averages also involved terms like

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-40870-1_9/439456_1_En_9_IEq4_HTML.gif

and

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-40870-1_9/439456_1_En_9_IEq5_HTML.gif

(8.59). All these expressions come from the definition of engineering moduli (Sect. 4.7) or similar magnitudes that involve more than one direction in their projection.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Fourth Rank Properties

What kind of engineering modulus, or which combination of them would this modulus correspond to?

Same question!

Can you calculate the latitudes of these parallels?

Because the angle \(\psi \) does not appear in the third row of Euler’s \(\underset{{{{\backsim }}}}{L}\). A similar discussion as above can be made for the use of the columns of \(\underset{{{{\backsim }}}}{L}\) as unit projection vectors. In this case, it is \(\varphi \) the one that does not appear in the third column.

Almost; see (9.10) below.

There is a good reason to choose this name, but it is of no relevance for the purposes of this book.

Can you write the \(\underset{{{{\backsim }}}}{L}\) for the transformation that brings the general \(\underline{\underline{A}}\) to the form (9.9)?

It can also be brought to any of the two other variants in which \(\lambda \) and \(-\lambda \) occupy the elements 13 or 23. In the first case, it is the axis ②that points along \(\underline{u}\), in the second, it is ①.

The sign of the vector product depends on the sign of the volume 3-form, in this case \(\underline{\underline{\underline{\epsilon }}}\), while the sign of the two-form onto which the vector product is mapped by duality does not.

Three and not two are needed, because \(\underline{u}\) is not of unit modulus, so three components are necessary, or two to specify its arbitrary orientation, one to specify its magnitude.

Or only five if absolute size is ignored.

Why is this not surprising?

Why?

Titel: Transversality and Skew Symmetric Properties
verfasst von: Manuel Laso
Nieves Jimeno
Verlag: Springer International Publishing
Buch: Representation Surfaces for Physical Properties of Materials
Print ISBN: 978-3-030-40869-5

Electronic ISBN: 978-3-030-40870-1

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-40870-1_9

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht