?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%2F589%2F&rft.title=Analysis+of+a+Model+for+Ship+Maneuvering&rft.creator=Apri%2C+M&rft.creator=Banagaay%2C+N&rft.creator=van+den+Berg%2C+J&rft.subject=Transport+and+Automotive&rft.subject=Machines+%2F+Production&rft.description=We+analyze+numerically+and+theoretically+steady+states+and+bifurcations+in+a+model+for+ship+maneuvering+provided+by+MARIN%2C+and+in+a+simplified+model+that+combines+rudder+and+propeller+into+an+abstract+%E2%80%98thruster%E2%80%99.+Steady+states+in+the+model+correspond+to+circular+motion+of+the+ship+and+we+compute+the+corresponding+radii.%0D%0AWe+non-dimensionalize+the+models+and+thereby+remove+a+number+of+parameters%2C%0D%0Aso+that%2C+due+to+a+scaling+symmetry%2C+only+the+rudder+(or+thruster)+angle+remains+as+a+free+parameter.%0D%0AUsing+%E2%80%98degree+theory%E2%80%99%2C+we+show+that+a+slight+modification+of+the+model+pos-%0D%0Asesses+at+least+one+steady+state+for+each+angle+and+find+certain+constraints+on+the+possible+steady+state+configuration.+We+show+that+straight+motion+is+unstable+for+the+Hamburg+test+case+and+use+numerical+continuation+and+bifurcation+software+to+compute+a+number+of+curves+of+states+together+with+their+stability%2C+and+the+corresponding+radii+of+the+ship+motion.+In+particular%2C+straight+forward+motion+can+be+stabilised+by+increasing+the+rudder+size+parameter%2C+and+the+smallest+possible+radius+is+%E2%88%BC+119+m.%0D%0AThese+analyses+illustrate+methods+and+tools+from+dynamical+systems+theory+that+can+be+used+to+analyse+a+model+without+simulation.+Compared+with+simulations%2C+the+numerical+bifurcation+analysis+is+much+less+time+consuming.+We+have+implemented+the+model+in+MATLAB+and+the+bifurcation+software+AUTO.&rft.date=2011&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%2F589%2F1%2FAmst114.pdf&rft.identifier=++Apri%2C+M+and+Banagaay%2C+N+and+van+den+Berg%2C+J++(2011)+Analysis+of+a+Model+for+Ship+Maneuvering.++%5BStudy+Group+Report%5D+++++