Where MRBis the rigid-body inertia matrix, Aistheinfinite-frequency added mass matrix, x(t)isthe
body’s acceleration,K is the retardation function matrix, x(t)is the body’s velocity, is the hydrostatic
restoring stiffness matrix, x(t) isthe body’s displacement, and exc (t)is the wave excitation force and any
other external loads, including viscous damping as a fraction of the critical damping.
The coefficients relating to the hydrodynamic added mass, damping and hydrostatic stiffness are
obtained from a frequency-domain analysis of the floating platform’s geometry. The wave excitation
forces as a function of incident wave frequency are also computed in this manner. One issue with Eqn.1
is that the convolution integral representing the radiation forces of the body is computationally inefficient.
One approach to solve this is to approximate the convolution integral with a state space model which is
inherently computationally efficient as discussed by Taghipour et al.[15] and Borg et al. [16].The
equations of motion now become: