CONTENTS (Continued) 
Page 
Chapter'8 ‘Conclusion for Part Ik .3..2320 00 ee oe ee ae 247 
Appendix Al _ Data for the Generation of the Processes ................... 251 
Appendix A2_ Polynomial Model Fitting to Observed Data ................ 261 
Part Dil 
‘Treatmentof Nonlinearities 2 306222 ol ce cee ie oes ores eevee reels 267 
Chapter 9 "Introduction oi. ace. ete Seas w otters ae ee oes aisle dane creed nae 267 
OriwaIntroductionfonbart Ml yey sere eee oot tei ietcit 267 
92 Nonlinearityjofi@ceam Waves! sac. ei solic els oa iin erence 268 
92.1 Second Order Spectrum of Waves by L. J. Tick and Others ............ 268 
ODE BiSDECInUMN Ofe WAVES ores se tarnrctare cuetee cael alerge eRe oe eee vey stems ane heeceae 271 
9.3 Response of the Behavior of a Marine Vehicle on Waves ................ 274 
9.4 Nonlinearity of the Behavior of Marine Vehicles ...................208- 277 
Chapter 10 Approximation Methods for the Analysis of Nonlinear 
System in Random Excitement ...................0-0e-ee eee 281 
XO Git lilayofolt (clio) 1 ae ane ME RAE MN SING oC uc KOU EAA obinn dy. Ob O's do didé cb ooo 281 
10.2 Equivalent Linearization Method .............. 0... cece eee eee ee 281 
10:3) sPerturbation Method iii f5yare:. cartoons et anercie ch merce art ote aisree teat yon rene 285 
LOSAG Trial for; Shipis Rolling sens so acer ery ee ee eee 285 
10.3.2 General Formulation of the Perturbation Method ..............+.+-- 288 
Chapter 11 Voltera Expansion and Application of Polyspectra............. 295 
Lm Voltera—W ener Expressions. cei crore ercrs nercnncrne re eens isroetete 295 
11.2 Higher Order Response Function, h,(T),T2,° - - Tn); Hn(@1,@2,° --@pn) ... 296 
11.3 Second Order Nonlinear Process Bispectrum, Cross Bispectrum ......... 297 
11.4 Characters of Quadratic Response to Gaussian Input Process ............ 302 
11°S) “Application(of the Higher, Orden Folyspectra. creer tree ieieier 316 
Chapter 12 Probabilistic Characters of Nonlinear Response Process ........ 325 
WAIL ilies Waite enadocotnbosond Gobo kd ndoodoDodbadodosdeoduodoad 325 
12.2 Markov-Process 2.5 5 sratsei cies, o0''s nye voleyel crataskelousgentomsioy conse erence ern eReneets 326 
123, | General(Process*sievemho pelosi Soieiei aoe ei on cree ee 328 
12.4. The Fokker—Planck Equation: (2.945 222,22).0)5 ts «clon is ate tet et 329 
12.5 Probability Characteristics of Amplitudes, Maxima and Minima ......... 336 
12.6 Application of the Fokker—Planck Equation for the Analysis 
of Seakeeping Datay i ..)s i522) kus creenarstonscieie eeeneracesio acl tenor rare 342 
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