ANALYTICAL EXPRESSIONS OF THE STABILITY AND BIFURCATION BOUNDARIES FOR GENERAL SPREAD MOORING SYSTEMS

Spread mooring systems (SMS) are labeled as general when they are not restricted by conditions of symmetry. The six necessary and sufficient conditions for stability of general SMS are derived analytically. The boundaries where static and dynamic loss of stability occur also are derived in terms of the system eigenvalues, thus providing analytical means for defining the morphogenesis that occurs when a bifurcation bo undary is crossed. The equations derived in this paper provide analyti cal expressions of elementary singularities and routes to chaos for ge neral mooring system configurations. Catastrophe sets are generated fi rst by the derived expressions and then numerically using nonlinear dy namics and codimension-one and -two bifurcation theory; agreement is e xcellent. The mathematical model consists of the nonlinear, third-orde r maneuvering equations without memory of the horizontal plane, slow-m otion dynamics-surge, sway, and yaw-of a vessel moored to several term inals. Mooring lines can be modeled by synthetic nylon ropes, chains, or steel cables. External excitation consists of time-independent curr ent, wind, and mean wave drift forces. The analytical expressions deri ved in this paper apply to nylon ropes and current excitation. Express ions for other combinations of lines and excitation can be derived.