Euler Angle from Body Frame to Inertial Frame?

I am trying to build a Simulink model for my quadcopter project.

I derived the equations of motion using the Newtown-Euler method in the body frame to get transnational and angular acceleration.

For the transnational part, I can simply use a rotation matrix to convert the accelerations back into the inertial frame.

But what about the rotational part?

Assuming that subscript n is the inertial frame and subscript c is the body frame. And then in the rotation matrix, c is cos and s is sin.

The equations on the top right are derived in body frame. I want to convert to inertial frame by transposing the rotation matrix in lower right. The rotation matrix is derived using Euler ZYX multiplication. The angles in the rotation matrix are inertial frame?

To run this process in a simulation loop, I will use the inertial angles from the previous loop for the rotation matrix to get current inertial angle?

Thanks,

Answer 1

[Christiaan]

Dear Yu Hin Hau,

If the transformation matrix from the inertial frame to the body frame is known, and you would like to know the transformation matrix from the the body frame to the inertial frame, you could use the MATLAB function transpose, to switch the indices of the transformation matrix. This is allowed, since the transformation matrix is orthogonal.

Good luck! Christiaan