FIGURES (Continued) 
Page 
Bispectrumlooceaniwavie nyse ei eee rere eee 273 
IRestorin pecOechhicientem es sei eer ciel tere rerreerer 282 
Spectra of wave, roll, and roll angular velocity ..................--- 289 
Linear response of roll to the exciting moment ..................... 289 
Convolution of spectrum Sjg 0... . ee ee eee eee ee eee ee 290 
Computed nonlinear spectrum of rolling ...................---.--- 290 
Symmetric character of bispecttum ................---++-+---ees 300 
An example of bispectrum of rolling of a ship on the sea ........ een he 301 
Winear resistance frequency; TESPONSE) .vayy-ilsteror sveree eiterelelet-eyeicdsienne cl 309 
Coefficients L; of linear resistance impulse response function ......... 310 
Estimate of G2(0,,—0.) from cross—bispectral analysis, Fn =0.15...... 310 
Isometric plot of modulus of wave—wave resistance 
Gross bispectrum) seaistate Bhi 10s) usta ts eieeeveeenelereler ene dener hele) oti 311 
Real part of wave—wave resistance cross spectrum, sea state B, 
Fn = 0.15 (normalization const. = 3.76 X 10) ................+:- 312 
Real part of estimated G2(0,,-0,), sea state B, Fn = 0.15 ............ 313 
Coefficient Qj of quadratic resistance impulse response function, 
value shown are 50 Qj, truncated to integer ..................0-000- 314 
Time history of waves and resistance observed and computed ......... S115) 
Amplitude response of two digital filters ........... 02. e ecu e ee eeee 316 
Simulated time histories of linear random excitation X(t) and 
nonlinear response Y(t), its component Y(t), Y2(t), 
Fil Ai yom WOR Gee Aho oicc Od OmOe Oooo HOD Ube bene dag adcodo od 321 
Mruncated linear discrete kemelsg7\istija let yee sy ae 321 
Truncated quadratic discrete kernel Si US Bet nas ere alain sua ty mustene ieee sales 322 
Portions of the truncated cubic discrete kernel Sixt a ieteslantes Aicyaleeeory oes 323 
Observed and predicted spectra and the components of spectrum of 
nonlinear response of the simulated system, nominal 0, =1.0 ........ 324 
Probability distribution density function of extremes ................ 338 
Displacement-force relation of set—up spring. ................ essen 341 
XiV 
