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

Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Get roll-pitch-yaw angles from the rotation matrix:

https://wolfram.com/xid/0do76e8rrc2pwajli-8lvk4l

https://wolfram.com/xid/0do76e8rrc2pwajli-g4sesa

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

https://wolfram.com/xid/0do76e8rrc2pwajli-hl0z3o

https://wolfram.com/xid/0do76e8rrc2pwajli-8n9w92

Scope (2)Survey of the scope of standard use cases
Get roll-pitch-yaw angles from a rotation matrix:

https://wolfram.com/xid/0do76e8rrc2pwajli-mbuhd2

https://wolfram.com/xid/0do76e8rrc2pwajli-kh62ql

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

https://wolfram.com/xid/0do76e8rrc2pwajli-oafd2i

https://wolfram.com/xid/0do76e8rrc2pwajli-dkx62l

Properties & Relations (1)Properties of the function, and connections to other functions
RollPitchYawAngles returns angles for which RollPitchYawMatrix gives the same rotation matrix:

https://wolfram.com/xid/0do76e8rrc2pwajli-baosc0

https://wolfram.com/xid/0do76e8rrc2pwajli-ce5rhy

The angles need not be the same:

https://wolfram.com/xid/0do76e8rrc2pwajli-jmeupz

https://wolfram.com/xid/0do76e8rrc2pwajli-gh9g1a

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

https://wolfram.com/xid/0do76e8rrc2pwajli-4l7ji

Possible Issues (1)Common pitfalls and unexpected behavior
RollPitchYawMatrix allows equal consecutive axes, and this generates a rotation matrix:

https://wolfram.com/xid/0do76e8rrc2pwajli-ew7s47


https://wolfram.com/xid/0do76e8rrc2pwajli-bt34u0

However, RollPitchYawAngles requires consecutive axes to be distinct:

https://wolfram.com/xid/0do76e8rrc2pwajli-g56qrp


This is because with consecutive axes equal, some rotation matrices cannot be represented:

https://wolfram.com/xid/0do76e8rrc2pwajli-hd2fbb


https://wolfram.com/xid/0do76e8rrc2pwajli-nrf78a


https://wolfram.com/xid/0do76e8rrc2pwajli-l3oy2l

Wolfram Research (2015), RollPitchYawAngles, Wolfram Language function, https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.
Text
Wolfram Research (2015), RollPitchYawAngles, Wolfram Language function, https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.
Wolfram Research (2015), RollPitchYawAngles, Wolfram Language function, https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.
CMS
Wolfram Language. 2015. "RollPitchYawAngles." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.
Wolfram Language. 2015. "RollPitchYawAngles." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RollPitchYawAngles.html.
APA
Wolfram Language. (2015). RollPitchYawAngles. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RollPitchYawAngles.html
Wolfram Language. (2015). RollPitchYawAngles. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RollPitchYawAngles.html
BibTeX
@misc{reference.wolfram_2025_rollpitchyawangles, author="Wolfram Research", title="{RollPitchYawAngles}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/RollPitchYawAngles.html}", note=[Accessed: 11-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_rollpitchyawangles, organization={Wolfram Research}, title={RollPitchYawAngles}, year={2015}, url={https://reference.wolfram.com/language/ref/RollPitchYawAngles.html}, note=[Accessed: 11-July-2025
]}