Wolfram Language & System 11.0 (2016)|Legacy Documentation

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EulerAngles

EulerAngles[r]
gives Euler angles {α,β,γ} corresponding to the rotation matrix r.

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

DetailsDetails

  • EulerAngles[r,{a,b,c}] gives angles {α,β,γ} 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 1, 2, or 3. 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:

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

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Introduced in 2015
(10.2)