The stability in the sense of Liapunov of the horizontal plane slow motions of Single Point Mooring (SPM) systems is studied. The mathematical model consists of the manoeuvering equations of the moored vessel and a nonlinear stress-strain relation for the mooring line. Steady excitation from current, wind and drift forces is included. Six first-order nonlinear coupled differential equations describe the system dynamics The system equilibria are first found and local analysis is performed in their vicinity. A SPM system, may asymptotically converge to a stable equilibrium, diverge from an unstable equilibrium or converge to a limit cycle. Due to the dependence of the eigenvalues of the system at each equilibrium on the system, parameters, the system may exhibit codimension-one bifurcations of pitchfork or Hopf type, or bifurcations of closed orbits. Based on the results of local analysis, the global system behaviour can be assessed, and design decisions can be made for selection of the principal SPM configuration parameters to avoid undesirable response. Finally the large-amplitude low-frequency motions observed in moored vessels, and often attributed to time-dependent external excitation, are explained using the results of the stability analysis.
Journal description