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2-18.16

rotation, of vector

URNurn:iso:std:iso:80000:-2:ed-2:en:item:2-18.16

https://metanorma.github.io/isq-smart/math/part-2-18/t2-18.16
urn:iso:std:iso:80000:-2:ed-2:en:item:2-18.16

ISQ Identifiers

ISO

urn:iso:std:iso:80000:-2:ed-2:en:item:2-18.16

IEC

urn:iec:std:iec:80000-2:2019:::item:2-18.16

Designations

ENrotation, of vector

FRrotationnel d'un vecteur

Symbol

\nabla \times a

rot a

Notation systems

AsciiMath

bb(grad) xx a

AsciiMath

bb("rot")" "bb(ii(a))

LaTeX

\mathbf{\nabla} \times a

LaTeX

\mathbf{\text{rot}} \text{ } \mathbf{\mathit{a}}

Definition

rotation of $a$

rotationnel de $a$

Notes

The coordinates are

${(\nabla \times a)}_{x} = \frac{\partial a_{z}}{\partial y} - \frac{\partial a_{y}}{\partial z}$

${(\nabla \times a)}_{y} = \frac{\partial a_{x}}{\partial z} - \frac{\partial a_{z}}{\partial x}$

${(\nabla \times a)}_{z} = \frac{\partial a_{y}}{\partial x} - \frac{\partial a_{x}}{\partial y}$

The operator $curl$ should be avoided and the operator $rot$ should be written in bold face.

${(\nabla \times a)}_{i} = \sum_{j} \sum_{k} ɛ_{i j k} \frac{\partial a_{k}}{\partial x_{j}}$

See Levi-Civita symbol.

Les coordonnées sont

${(\nabla \times a)}_{x} = \frac{\partial a_{z}}{\partial y} - \frac{\partial a_{y}}{\partial z}$

${(\nabla \times a)}_{y} = \frac{\partial a_{x}}{\partial z} - \frac{\partial a_{z}}{\partial x}$

${(\nabla \times a)}_{z} = \frac{\partial a_{y}}{\partial x} - \frac{\partial a_{x}}{\partial y}$

Il convient d'éviter l'opérateur $curl$ et il convient d'écrire l'opérateur $rot$ en caractères gras.

${(\nabla \times a)}_{i} = \sum_{j} \sum_{k} ɛ_{i j k} \frac{\partial a_{k}}{\partial x_{j}}$

Voir Levi-Civita symbol.

Ontology
isq:MathConcept smart:TermEntry

Class Hierarchy

smart:Entity smart:TermEntryisq:MathConcept

A mathematical concept as defined in ISO/IEC 80000 Part 2.

Instance IRI

isq:t2-18.16

Properties

isq:MathConceptShape

Property	Value
rdf:type	isq:MathConcept smart:TermEntry
dcterms:identifier	2-18.16
skosxl:prefLabel	"rotation, of vector"@en
skosxl:altLabel	"bb(grad) xx a"@en"bb("rot")" "bb(ii(a))"@en
skos:definition	rotation of stem:[bb(ii(a))]
skos:note	The coordinates are stem:[(bb(grad) xx bb(ii(a)))_x = (del a_z)/(del y) - (del a_y)/(del z)] stem:[(bb(grad) xx bb(ii(…
smart:hasBindingnessType	bindingness-type:normative
dcterms:isPartOf	isq:part-2-18

Related Entities

isq:MathConceptShape isq:part-2-18 smart:TermEntry