I will be honest. I basically registered here, to get a question answered which is bothering me a lot lately. Would be really nice if someone could help me a little. So lets cut right to the case

Assuming you have an aircraft with a propellor on each wing.

And lets say, the aircraft as well as the rotors rotate at an angluar velocity (Wx,Wy Wz - for the aircraft & Nx,Ny,Nz - for the rotor).

The rotor can only rotate about its X-axis (so for example Nx=100 rad/s, Ny=0, Nz=0) and the aircraft can rotate freely about all of its 3 axis (I dont know, something like Wx=0 rad/s, Wy=0, Wz=0.5 --> So we are yawing).

Aircraft frame is (X=Roll, Y=Pitch, Z=Yaw)

The time t is set to 1s.

Now... what is the angluar velocity of the propellor center of gravity combining both rotations (aircraft & prop)?

What i found is this general formulation: (R = angular velocity at prop CoG)

Rx = Wx + Nx

Ry = Wy * cos(Nx * t) + Wz * sin(Nx * t)

Rz = -Wy * sin(Nx * t) + Wz * cos(Nx * t)

I think it makes sense, but i dont quite get fully behind the calculation of Ry & Rz. Can someone please help me to fully understand those two lines. I can add some illustrations/visualizations if needed.

Thanks!