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Equation (4.49) is the matrix form of the motion equations in frequency domain. This matrix form equation not only covers the coupling effects between heave and pitch, but also may include all couplying effects between all the rigid body 6 degree of freedom motions.Â

In frequency domain, the acceleration RAO, a, is -omage**2 *x, the velocity RAO, v, is -i*omega*x, where x is the motion response RAO (could be heave z or pitch angle). Substituting these expressions into the equations (1) and (2) in the journal you cited, they will be similar to Equation (4.49). I guess that in equation (2) A is the sum of the pitch-pitch moment of inertia and the pitch-pitch added mass.