Wolfram Language & System 11.0 (2016)|Legacy Documentation

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

RollPitchYawAngles

RollPitchYawAngles[r]
gives the roll-pitch-yaw angles {α,β,γ} corresponding to the rotation matrix r.

RollPitchYawAngles[r,{a,b,c}]
gives the roll-pitch-yaw angles {α,β,γ} corresponding to rotation order {a,b,c}.

DetailsDetails

  • RollPitchYawAngles is used to decompose into fixed axis-oriented rotations.
  • RollPitchYawAngles[r,{a,b,c}] gives angles {α,β,γ} such that RollPitchYawMatrix[{α,β,γ},{a,b,c}]r.
  • RollPitchYawAngles[r] is equivalent to RollPitchYawAngles[r,{3,2,1}], the z-y-x rotation.
  • The default z-y-x angles RollPitchYawAngles[r,{3,2,1}] decompose 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
    {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 (default)
  • 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 roll-pitch-yaw angles from the rotation matrix:

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Get roll-pitch-yaw angles from the rotation matrix with the given rotation order:

In[1]:=
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Introduced in 2015
(10.2)