# RollPitchYawAngles

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}.

# Details   • 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.
• 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.

# Examples

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## Basic Examples(2)

Get roll-pitch-yaw angles from the rotation matrix:

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

## Scope(2)

Get roll-pitch-yaw angles from a rotation matrix:

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

## Properties & Relations(1)

RollPitchYawAngles returns angles for which RollPitchYawMatrix gives the same rotation matrix:

The angles need not be the same:

However, both sets of angles produce the same rotation matrix:

## Possible Issues(1)

RollPitchYawMatrix allows equal consecutive axes, and this generates a rotation matrix:

However, RollPitchYawAngles requires consecutive axes to be distinct: This is because with consecutive axes equal, some rotation matrices cannot be represented: