I am trying to analyse response of a dynamic system. The source disturbance is about x,y,theta (rotation about x ) & Phi of one coordinate system (red coloured coordinate system in the attached figure). I need to get the response in another coordinate system ( green coloured coordinate system in the attached figure), whose all three axis is inclined to initial coordinate system. In case of only x & y,it can be easily done using transformation matrix, but how to handle the transformation of rotational dof. I tried to convert the source disturbance in spherical coordinate system , then cartesian, then transformation and finally again to (X, Y, Z, THETA, PHI, PSI,) new coordinate system; but this process is to tedious. Is there any better alternative is available ?