Wolfram Language & System 10.3 (2015)|Legacy Documentation

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

RollPitchYawMatrix

RollPitchYawMatrix[{α,β,γ}]
gives the 3D rotation matrix formed by rotating α around the initial axis, then β around the initial axis, and then γ around the initial axis.

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

DetailsDetails

  • RollPitchYawMatrix is also known as bank-elevation-heading matrix or Cardan matrix. The angles 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},{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 , , or , 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.
Introduced in 2015
(10.2)