Dear Fatemeh,
The forum topic I linked above (OC3-Hywind RAOs) shows how to transform the 6x6 mass/center of mass/inertia matrix from the SWL to CG i.e.:
M_cg = TransMat^TM_swlTransMat
where,
TransMat =
[ [ 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 ] ]
and
TransMat^T =
[ [ 1 0 0 0 0 0 ];
[ 0 1 0 0 0 0 ];
[ 0 0 1 0 0 0 ];
[ 0 z_cg -y_cg 1 0 0 ];
[ -z_cg 0 x_cg 0 1 0 ];
[ y_cg -x_cg 0 0 0 0 1 ] ]
A general 6x6 mass matrix is written as shown in the image below, where the 3x3 inertia submatrix is defined about the origin of the coordinate system (not the CG).
Best regards,
