Dear Carlo,
I don’t believe your M_cg is correct. The mass matrix about the cg should be basically a diagonal matrix (with maybe some small nonzero off-diagonal terms in the lower-right inertia quadrant). The mass matrix of the OC3-Hywind spar system about the SWL is given in my Nov 16, 2012 post in the following forum topic: Inertial Moments of OC3-Hywind Components.
I’m not sure what you mean when you say the “additional stiffness remains the same”, but as my prior post explains, the mass (M), added mass (A), damping (B), stiffness (C), force (F), and displacement (q) all get transformed between SWL and CG.
To convert RAOs from the CG to the SWL, you could write:
q_swl = TransMat^-1*q_cg
where,
TransMat^-1 =
[ [ 1 0 0 0 z_cg -y_cg ];
[ 0 1 0 -z_cg 0 x_cg ];
[ 0 0 1 y_cg -x_cg 0 ];
[ 0 0 0 1 0 0 ];
[ 0 0 0 0 1 0 ];
[ 0 0 0 0 0 1 ] ]
Your equation is almost correct, except that “roll” should be changed to “pitch”.
Best regards,