RollPitchYawAngles

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`RollPitchYawAngles`

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RollPitchYawAngles[r]

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

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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.
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

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Basic Examples (2)Summary of the most common use cases

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

In[1]:=1

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

In[2]:=2

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

Out[2]=2

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

In[1]:=1

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

In[2]:=2

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

Out[2]=2

Scope (2)Survey of the scope of standard use cases

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

In[1]:=1

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

In[2]:=2

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

Out[2]=2

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

In[1]:=1

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

In[2]:=2

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

Out[2]=2

Properties & Relations (1)Properties of the function, and connections to other functions

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

In[1]:=1

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

In[3]:=3

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

Out[3]=3

The angles need not be the same:

In[4]:=4

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

In[6]:=6

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

Out[6]=6

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

In[7]:=7

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

Out[7]=7

Possible Issues (1)Common pitfalls and unexpected behavior

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

In[1]:=1

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

Out[1]=1

In[2]:=2

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

Out[2]=2

However, RollPitchYawAngles requires consecutive axes to be distinct:

In[3]:=3

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

Out[3]=3

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

In[4]:=4

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

Out[4]=4

In[5]:=5

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

Out[5]=5

In[6]:=6

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

Out[6]=6

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