see [3, section 8.2.4]. Here Mpq are the elements of the mass matrix, is the density of the fluid,and the constants cpq and pq describe the characteristics of respectively the springs and dampers in the moorings; appropriate buoyancy contributions are included in the spring coefficients (only heave, roll and pitch motions induce non-zero buoyancy forces). The first term on the right-hand side of (11) is the hydrodynamic force arising from the fluid motion, and Fp(t) is an external force
(not related to the fluid motion or the moorings) applied in mode p. In addition, for each p the initial displacement Xp(0) and velocity Vp(0) of the structure must be prescribed.