Three‐Dimensional Coupled Dynamics of a Buoy and Multiple Mooring Lines: Formulation and Algorithm

The equations of the coupled three‐dimensional motion of a submerged buoy and multiple mooring lines are formulated using Kane's formalism. The lines are modelled using lumped masses and tension‐only springs including structural damping. Surface waves are described by Stokes's second‐order wave theory. The hydrodynamic loads due to viscous drag are applied via a Morison's equation approach using the instantaneous relative velocities between the fluid field and the bodies (buoy and lines). The detailed algorithm is presented and the equations are solved using a robust implementation of the Runge–Kutta method provided in MATLAB. The mathematical model and associated algorithm are validated by comparison with special cases of an elastic catenary mooring line and other published data.