Analysis of a model for ship maneuvering

M. Apri, N. Banagaaya, J.B. Berg, van den, R. Brussee, D.P. Bourne, T. Fatima, F. Irzal, J.D.M. Rademacher, B. Rink, F. Veerman, S. Verpoort

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We analyze numerically and theoretically steady states and bifurcations in a model for ship maneuvering provided by MARIN, and in a simpli¿ed model that combines rudder and propeller into an abstract ‘thruster’. Steady states in the model correspond to circular motion of the ship and we compute the corresponding radii. We non-dimensionalize the models and thereby remove a number of parameters, so that, due to a scaling symmetry, only the rudder (or thruster) angle remains as a free parameter. Using ‘degree theory’, we show that a slight modi¿cation of the model possesses at least one steady state for each angle and ¿nd certain constraints on the possible steady state con¿guration. 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, and the corresponding radii of the ship motion. In particular, straight forward motion can be stabilised by increasing the rudder size parameter, and the smallest possible radius is ~ 119 m. These analyses illustrate methods and tools from dynamical systems theory that can be used to analyse a model without simulation. Compared with simulations, the numerical bifurcation analysis is much less time consuming. We have implemented the model in MATLAB and the bifurcation software AUTO.
Original languageEnglish
Title of host publicationProceedings of the 79th European Study Group Mathematics with Industry (Amsterdam, The Netherlands, January 24-28, 2011)
EditorsB. Planqué, S. Bhulai, J. Hulshof, W. Kager, T. Rot
Place of PublicationAmsterdam
PublisherVrije Universiteit Amsterdam
Publication statusPublished - 2012
Event79th European Study Group with Industry, January 24-28, 2011, Amsterdam, The Netherlands - Amsterdam, Netherlands
Duration: 24 Jan 201128 Jan 2011


Conference79th European Study Group with Industry, January 24-28, 2011, Amsterdam, The Netherlands
OtherEuropean Study Group with Industry


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