Euler angles - Revision history

Karl Jones at 23:49, 24 April 2016

2016-04-24T23:49:02Z

Karl Jones: /* External links */

2016-04-24T23:48:13Z

‎External links

Karl Jones at 16:27, 5 February 2016

2016-02-05T16:27:22Z

Karl Jones at 16:26, 5 February 2016

2016-02-05T16:26:49Z

Karl Jones: Created page with "The '''Euler angles''' are three angles introduced by Leonhard Euler to describe the orientation of a rigid body (TO DO: fix math, expand,..."

2015-09-14T10:45:53Z

Created page with "The '''Euler angles''' are three angles introduced by Leonhard Euler to describe the orientation of a rigid body (TO DO: fix math, expand,..."

New page

The '''Euler angles''' are three angles introduced by [[Leonhard Euler]] to describe the [[Orientation (geometry)|orientation]] of a [[rigid body]]

(TO DO: fix math, expand, organize, cross-reference, illustrate.)

== Description ==

To describe such an orientation in [[dimension|3-dimensional]] [[Euclidean space]] three parameters are required.

They can be given in several ways, Euler angles being one of them; see [[charts on SO(3)]] for others.

Euler angles are also used to describe the orientation of a [[frame of reference]] (typically, a [[coordinate system]] or [[Basis (linear algebra)|basis]]) relative to another. They are typically denoted as [[Alpha|{{math|''α''}}]], [[Beta|{{math|''β''}}]], [[Gamma|{{math|''γ''}}]], or [[Phi|{{math|''φ''}}]], [[Theta|{{math|''θ''}}]], [[Psi (letter)|{{math|''ψ''}}]].

Euler angles represent a sequence of three ''[[elemental rotation]]s'', i.e. rotations about the axes of a [[coordinate system]].

For instance, a first rotation about {{math|''z''}} by an angle {{math|''α''}}, a second rotation about {{math|''x''}} by an angle {{math|''β''}}, and a last rotation again about {{math|''z''}}, by an angle {{math|''γ''}}. These rotations start from a known standard orientation.

In physics, this standard initial orientation is typically represented by a motionless (''fixed'', ''global'', or ''world'') [[coordinate system]]; in [[linear algebra]], by a [[standard basis]].

Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system ([[#Extrinsic rotations|extrinsic rotations]]) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation ([[#Intrinsic rotations|intrinsic rotations]]).

The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a ''local'' coordinate system.

== See also ==

* [[Mathematics]]

== External links ==

* [https://en.wikipedia.org/wiki/Euler_angles Euler angles] @ Wikipedia

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 The '''Euler angles''' are three angles introduced by [[Leonhard Euler]] to describe the [[Orientation (geometry)|orientation]] of a [[rigid body]].
 == See also ==
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 * [[Leonhard Euler]]
 * [[Mathematics]]
 == External links ==
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 * [https://en.wikipedia.org/wiki/Euler_angles Euler angles] @ Wikipedia
 [[Category:Mathematics]]

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	* [https://en.wikipedia.org/wiki/Euler_angles Euler angles] @ Wikipedia		* [https://en.wikipedia.org/wiki/Euler_angles Euler angles] @ Wikipedia
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−	The '''Euler angles''' are three angles introduced by [[Leonhard Euler]] to describe the [[Orientation (geometry)\|orientation]] of a [[rigid body]]	+	The '''Euler angles''' are three angles introduced by [[Leonhard Euler]] to describe the [[Orientation (geometry)\|orientation]] of a [[rigid body]].
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	== Description ==		== Description ==