# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# EulerAngles

EulerAngles[r]
gives Euler angles corresponding to the rotation matrix r.

EulerAngles[r,{a,b,c}]
gives Euler angles with rotation order .

## DetailsDetails

• EulerAngles[r,{a,b,c}] gives angles such that EulerMatrix[{α,β,γ},{a,b,c}]r.
• EulerAngles[r] is equivalent to EulerAngles[r,{3,2,3}], the z-y-z rotations.
• The default z-y-z angles EulerAngles[r,{3,2,3}] decomposes rotation into three steps:
• The rotation axes a, b, and c can be any integer , , or . But there are only twelve combinations that are general enough to be able to specify any 3D rotation.
• Rotations with the first and last axis repeated:
•  {3,2,3} z-y-z rotation (default) {3,1,3} z-x-z rotation {2,3,2} y-z-y rotation {2,1,2} y-x-y rotation {1,3,1} x-z-x rotation {1,2,1} x-y-x rotation
• Rotations with all three axes different:
•  {1,2,3} x-y-z rotation {1,3,2} x-z-y rotation {2,1,3} y-x-z rotation {2,3,1} y-z-x rotation {3,1,2} z-x-y rotation {3,2,1} z-y-x rotation
• Rotations with subsequent axes repeated may not be invertible since these are not capable of representing all possible rotations in 3D.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Get Euler angles from the rotation matrix:

 Out[2]=

Get Euler angles from the rotation matrix with the given rotation order:

 Out[2]=