?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F592%2F&rft.title=Dynamical+Models+of+Extreme+Rolling+of+Vessels+in+Head+Waves&rft.creator=Archer%2C+C&rft.creator=van+Daalen%2C+E&rft.creator=Dobbersch+%CC%88tz%2C+S&rft.subject=Transport+and+Automotive&rft.subject=Machines+%2F+Production&rft.subject=Fluids&rft.description=Rolling+of+a+ship+is+a+swinging+motion+around+its+length+axis.+In+particular+vessels+transporting+containers+may+show+large+amplitude+roll+when+sailing+in+seas+with+large+head+waves.+The+dynamics+of+the+ship+is+such+that+rolling+interacts+with+heave+being+the+motion+of+the+mass+point+of+the+ship+in+vertical+direction.+Due+to+the+shape+of+the+hull+of+the+vessel+its+heave+is+influenced+considerably+by+the+phase+of+the+wave+as+it+passes+the+ship.+The+interaction+of+heave+and+roll+can+be+modeled+by+a+mass-spring-pendulum+system.+The+effect+of+waves+is+then+included+in+the+system+by+a+periodic+forcing+term.+In+first+instance+the+damping+of+the+spring+can+be+taken+infinitely+large+making+the+system+a+pendulum+with+an+in+vertical+direction+periodically+moving+suspension.+For+a+small+angular+deflection+the+roll+motion+is+then+described+by+the+Mathieu+equation+containing+a+periodic+forcing.+If+the+period+of+the+solution+of+the+equation+without+forcing+is+about+twice+the+period+of+the+forcing+then+the+oscillation+gets+unstable+and+the+amplitude+starts+to+grow.+After+describing+this+model+we+turn+to+situation+that+the+ship+is+not+anymore+statically+fixed+at+the+fluctuating+water+level.+It+may+move+up+and+down+showing+a+motion%0D%0Amodeled+by+a+damped+spring.+One+step+further+we+also+allow+for+pitch%2C+a+swinging+motion+around+a+horizontal+axis+perpendicular+to+the+ship.+It+is+recommended+to+investigate+the+way+waves+may+directly+drive+this+mode+and+to+determine+the+amount+of+energy+that+flows+along+this+path+towards+the+roll+mode.+Since+at+sea+waves+are+a+superposition+of+waves+with+different+wavelengths%2C+we+also+pay+attention+to+the+properties+of+such+a+type+of+forcing+containing+stochastic+elements.+It+is+recommended+that+as+a+measure+for+the%0D%0Aoccurrence+of+large+deflections+of+the+roll+angle+one+should+take+the+expected+time+for+which+a+given+large+deflection+may+occur+instead+of+the+mean+amplitude+of+the+deflection.&rft.date=2009&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F592%2F1%2FWag1.pdf&rft.identifier=++Archer%2C+C+and+van+Daalen%2C+E+and+Dobbersch+%CC%88tz%2C+S++(2009)+Dynamical+Models+of+Extreme+Rolling+of+Vessels+in+Head+Waves.++%5BStudy+Group+Report%5D+++++