angular - Transform Rotation Velocity Relative to a Certain Coordinate Sytem into a Rotation Velocity Relative to another Coordinate Sytem

Question

So I have a Case:

1. I have two 3D Coordinate Sytems:
   • Real World(Rigid) Coordinate System ~ the Origin of all objects.
   • Certain Object's Local Coordinate System ~ since the object can move or rotate, this 3D coordinate system changes its position and orientations.
2. An Object is found at the Origin(0.0,0.0,0.0).
3. The Variables are:
   • α, β, γ = Pitch(X-Axis), Roll(Y-Axis), Yaw(Z-Axis) ~ Intrinsic Rotations of the Object's Local Coordinate System, from the Real World Coordinate System.
   • u, v, w = rotation velocity of the Object Relative to the Real World Coordinate System.
   • x, y, z = rotation velocity of the Object Relative to the Object's Local Coordinate System.
4. The First Trial was:
   • When the two coordinate systems are in phase(α = 0.0, β = 0.0, γ = 0.0)
   • Then the rotation velocities of the object on both coordinate systems are equal(x = u, y = v, z = w)
5. The Second Trial was:
   • When Object's Local Coordinate System was rotated(α = 131.42, β = -36.7, γ = 317.22)
   • And u = 14.2, v = 5.2, w = -1.32
   • Then x = ?, y = ?, z = ?

I am trying to get the Rotation Velocity of the Object relative to the its Local Coordinate System. I will appreciate the help of the community!

question from:https://stackoverflow.com/questions/65874622/transform-rotation-velocity-relative-to-a-certain-coordinate-sytem-into-a-rotati

Answer 1

Waitting for answers