# RollPitchYawMatrix

RollPitchYawMatrix[{α,β,γ}]

gives the 3D rotation matrix formed by rotating by α around the initial axis, then by β around the initial axis, and then by γ around the initial axis.

RollPitchYawMatrix[{α,β,γ},{a,b,c}]

gives the 3D rotation matrix formed by rotating by α around the fixed a axis, then by β around the fixed b axis, and then by γ around the fixed c axis.

# Details   • RollPitchYawMatrix is also known as bank-elevation-heading matrix or Cardan matrix. The angles {α,β,γ} are often referred to as Cardan angles, nautical angles, bank-elevation-heading, or roll-pitch-yaw.
• RollPitchYawMatrix is typically used to specify a rotation as a sequence of basic rotations around coordinate axes where each rotation is referring to the initial or extrinsic coordinate frame.
• RollPitchYawMatrix[{α,β,γ}] is equivalent to RollPitchYawMatrix[{α,β,γ},{3,2,1}].
• RollPitchYawMatrix[{α,β,γ},{a,b,c}] is equivalent to where Rα,a=RotationMatrix[α,UnitVector[3,a]] etc.
• The default z-y-x rotation RollPitchYawMatrix[{α,β,γ},{3,2,1}]:
• • 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 still produce a rotation matrix, but cannot be inverted uniquely using RollPitchYawAngles.

# Examples

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## Basic Examples(2)

The standard roll-pitch-yaw matrix:

 In:= Out//MatrixForm= Rotate an axes-aligned unit cube:

 In:= In:= Out= ## Neat Examples(2)

Introduced in 2015
(10.2)