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.