The analysis in this chapter of marine platform motions is directly applicable to any floating system such as ships, offshore platforms, floating wind turbines, or wave energy devices. The basic underlying model is the classic linear spring-mass-damper system. The mass will be augmented by the added mass of the fluid; the damping will be the result of the dissipation of energy by waves; the linear spring will be due to hydrostatic effects plus any external stiffness such as mooring lines; and the exciting forces are due to incident waves. Depending on the body shape and mass distribution, the equations of motion can be dynamically/statically coupled. Wave excitation is comprised of Froude-Krylov and diffraction components. Solutions to the equations of motion in the frequency domain are expressed as RAO’s. The RAO is a linear operator representing the dynamic response of a system (e.g. displacement, acceleration, bending moment, etc.) per unit input, typically the incident wave amplitude. Once the rigid body dynamics are expressed as RAO’s, other quantities or dynamics of interest may be determined, e.g. relative motion, dynamic bending and shear.

Chapter 5 is mainly devoted to the interaction between waves and immersed bodies. In general, an immersed body may oscillate in six different modes, three translating modes (surge, sway, heave) and three rotating modes (roll, pitch, yaw). An oscillating body radiates waves, and an incident wave may induce a corresponding excitation force for each one of the six modes. When a body oscillates, it radiates waves. Such radiated waves and excitation forces are related by so-called reciprocity relationships. Such relations are derived not only for a single oscillating body but even for a group (or 'array') of immersed bodies. Axisymmeric bodies and two-dimensional bodies are discussed in separate sections of the chapter. Although most of this chapter discusses wave-body dynamics in the frequency domain, a final section treats an immersed body in the time domain.