About: Euler's rotation theorem

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Euler's rotation theorem Goto Sponge Distinct Permalink

An Entity of Type : owl:Thing, within Data Space : el.dbpedia.org associated with source document(s)

In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a rotation group.

Attributes	Values
rdf:type	Thing
rdfs:label	Euler's rotation theorem (en)
rdfs:comment	In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a rotation group. (en)
rdfs:seeAlso	Rotation dbr:4-dimensional_Euclidean_space
sameAs	Euler's rotation theorem Euler's rotation theorem
dbp:wikiPageUsesTemplate	dbt:= dbt:Cite_journal dbt:Clear dbt:Efn dbt:Main dbt:Math dbt:Mvar dbt:Notelist dbt:Refimprove dbt:See_also dbt:Sfrac dbt:Short_description dbt:Sup dbt:Citizendium dbt:Leonhard_Euler
Subject	Euclidean symmetries Rotation in three dimensions Theorems in geometry Leonhard Euler
thumbnail	wiki-commons:Special:FilePath/Euler_AxisAngle.png?width=300
foaf:depiction
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Euler's_rotation_theorem?oldid=1073598724&ns=0
Wikipage page ID	865138 (xsd:integer)
page length (characters) of wiki page	29195 (xsd:nonNegativeInteger)
Wikipage revision ID	1073598724 (xsd:integer)
Link from a Wikipage to another Wikipage	Group (mathematics) Normal matrix Projection (linear algebra) Rotation (mathematics) Rotation around a fixed axis Rotation formalisms in three dimensions Rotation matrix Round-off error Unit vector 3D rotation group Angular frequency Axis–angle representation Three-dimensional space Three-dimensional graph Euclidean symmetries Rotation in three dimensions Theorems in geometry Geometry Leonhard Euler Direction cosine Leonhard Euler Quaternion Screw axis Screw theory Change of basis Characteristic polynomial Chasles' theorem (kinematics) Kinematics Plane of rotation Complex conjugate Complex number Computer graphics Eigenvalues and eigenvectors Orthogonal matrix Spherical geometry Spherical trigonometry Equivalence relation Fixed-point subgroup Improper rotation Kernel (linear algebra) Determinant Instant centre of rotation Trace (linear algebra) Vector (mathematics and physics) Euler angles Euler–Rodrigues formula Lie algebra Expm Rigid body William Rowan Hamilton
has abstract	In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a rotation group. The theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry. The axis of rotation is known as an Euler axis, typically represented by a unit vector ê. Its product by the rotation angle is known as an axis-angle vector. The extension of the theorem to kinematics yields the concept of instant axis of rotation, a line of fixed points. In linear algebra terms, the theorem states that, in 3D space, any two Cartesian coordinate systems with a common origin are related by a rotation about some fixed axis. This also means that the product of two rotation matrices is again a rotation matrix and that for a non-identity rotation matrix one eigenvalue is 1 and the other two are both complex, or both equal to −1. The eigenvector corresponding to this eigenvalue is the axis of rotation connecting the two systems. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Euler's_rotation_theorem
is Wikipage redirect of	Euler's fixed point theorem Euler fixed point theorem Euler rotation theorem Euler Pole
is Link from a Wikipage to another Wikipage of	List of theorems

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software