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absolute value added mass added-dynamic Amplitude of response analog computer angular frequency approximately barge heading barge motions bilge keels boom angle boom azimuth angle boom-lowered load Cartesian coordinate system center of gravity center-lowered load coefficient coefficient of correlation complex conjugate complex envelope complex plane complex response operators component considered convex hull correlation coefficient Correlation Function corresponding covariance covariance functions cross-covariance cross-spectral damping damping factor degrees of freedom differential equations direction displacement vector dynamic position effects energy density function energy spectrum energy-density equations equations of motion expected value feet Figure forces and moments free surface frequency Gaussian Gaussian stochastic process given heading angle HEADING degrees heaving motion height However hydrodynamic hydrostatic inertia instantaneous amplitude instantaneous frequency instantaneous phase difference joint probability distributions lateral motions line tension linear linear combinations long wave longitudinal lowering line marginal probability maximum mean metacentric height moment of inertia mooring cables Mooring spring mooring system motions in regular Neumann normal distribution obtained Ocean Surface Waves orbital velocities ordinate ordinate levels oscillations pair parameters phase shift pitch pitch moment present study probability density function probability distribution quantities r. m. s. values radians radians per second random variables ratio Rayleigh distribution relative to barge response amplitude operator response for unit-amplitude RMS values roll moment root-mean-square seaway section beam ship motions shown significant wave height sine waves sinusoidal waves slender-body theory SNAME Solid Mechanics spectral density spectral energy density spectral energy distribution spectral theory spring constant standard deviation stochastic process surface elevation surge sway theory time-history curve time-history functions total energy unit circle unit-amplitude wave velocity vertical load acceleration vertical load displacement wave heading wave length wave propagation wave relative wavelengths Westinghouse Electric Corporation wind York University zero