Ship Model for Parametric Roll Incorporating the Effects of Time-Varying Speed

  • Dominik A. BreuEmail author
  • Christian Holden
  • Thor I. Fossen


In this work, we develop a ship model for parametric roll resonance under non-constant speed. Variations in speed changes the encounter frequency, i.e., the Doppler-shifted frequency of the waves as seen from the ship. Commonly, a Mathieu-type equation is used to describe the ship dynamics in parametric roll resonance; however, the derivation of this model assumes constant encounter frequency. In this chapter, we show that Mathieu-type equations are not able to accurately capture the dynamics of the ship if the encounter frequency is subject to changes. We derive a highly accurate six-degree-of-freedom computer model of the ship and use this to verify a simplified one-degree-of-freedom analytical model, valid also for a non-constant encounter frequency.


Inertial Frame Roll Motion Body Frame Ship Model Forward Speed 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank our colleague Øyvind Ygre Rogne for his assistance with the code for finding the submerged part of the hull. This work was funded by the Centre for Ships and Ocean Structures (CeSOS), NTNU, Norway and the Norwegian Research Council.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Dominik A. Breu
    • 1
    Email author
  • Christian Holden
    • 1
  • Thor I. Fossen
    • 2
    • 1
  1. 1.Centre for Ships and Ocean StructuresNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of Engineering CyberneticsNorwegian University of Science and TechnologyTrondheimNorway

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