Analysis of a model for ship maneuvering

Apri, M. et al. (2012) Analysis of a model for ship maneuvering. In: Planque, B., Bhulai, S., Hulshof, J., Kager, W. and Rot, T. (eds.) Proceedings of the 79th European Study Group Mathematics with Industry. VU Publishing: Amsterdam, The Netherlands, pp. 83-116. ISBN 9789086596256

Abstract

We analyze numerically and theoretically steady states and bifurcations in a model for ship maneuvering provided by MARIN, and in a simplified 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. <p/>Using ‘degree theory’, we show that a slight modification of the model possesses 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, 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. <p/>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.

• Item Type: Book Sections
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bourne, Dr David
• Authors: Apri, M., Banagaaya, N., van den Berg, J.B., Brussee, R., Bourne, D., Fatima, T., Irzal, F., Rademacher, J., Rink, B., Veerman, F., and Verpoort, S.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Publisher: VU Publishing
• ISBN: 9789086596256
• Published Online: 01 January 2012