Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)

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.
Introduced in 2015
(10.2)