Fluid Dynamics and Ship Motion

  • Antonio Romano
  • Addolorata Marasco
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


This chapter is a brief introduction to the very difficult problem of ship motion. The difficulties of this problem are due to the many factors determining the behavior of a ship during the navigation: the form of the ship, the sea waves, the wind action, etc. After introducing the roll, pitch, and yaw angles, many fundamental kinematic relations are determined. Then, the dynamical equations are proposed starting from dynamics of rigid bodies. A section is dedicated to the analysis of the forces acting on the ship. Since the nonlinear problem posed by these equations is very difficult to solve, small motions are considered which lead to linear differential equations. All the forces and momenta, describing the actions of weight, buoyant force, the interaction between ship and sea, are taken into account. In order to evaluate all the terms appearing in the motion equations, it is necessary to consider the effects produced by waves propagating on the free surface of the sea. To the analysis of the wave propagation on the free surface are dedicated the last sections of the chapter.


Buoyant Force Free Boundary Problem Body Frame Pitch Motion Simple Wave 
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  1. [2]
    R. Bhattacharrya, Dynamics of marine vehicles (Wiley, New York, 1978)Google Scholar
  2. [14]
    O. Grim, A Method for a more precise computation of heaving and pitching motions, both in smooth water and in waves, in: Proc. Symp. Nav. Hydrodyn., 3rd ACR-65, Off. Nav. Res., Washington, DC (1960)Google Scholar
  3. [21]
    R.A. Ibrahim, I.M. Grace, Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch. Mathematical Problems in Engineering, vol. 2010 (Hindawi Publishing Corporation, 2009)Google Scholar
  4. [24]
    F. John, On the motion of floating bodies - Part I. Comm. Pure Appl. Math. 2, (1949)Google Scholar
  5. [25]
    F. John, On the motion of floating bodies - Part II. Comm. Pure Appl. Math. 3, (1950)Google Scholar
  6. [41]
    R. Nabergoj, Fondamenti di tenuta della nave al mare (Notes Trieste, 2010)Google Scholar
  7. [42]
    J.N. Newman, Theory of ship motions. Adv. Appl. Mech. 18, (1978)Google Scholar
  8. [44]
    J.R. Paulling, R.M. Rosenberg, On unstable ship motions resulting from nonlinear coupling. J. Ship Res. 3, (1959)Google Scholar
  9. [46]
    A.S. Peters, J.J. Stoker, The motion of a ship as a floating rigid body in a seaway. Comm. Pure Appl. Math. 10, (1957)Google Scholar
  10. [47]
    T. Perez, Ship Motion Control: Course Keeping and Roll Stabilisation Using Rudder and Fins (Springer-Verlag London, 2005)Google Scholar
  11. [48]
    W.G. Price, R.E.D. Bishop, Probabilistic Theory of Ship Dynamics (Chapman and Hall, London, 1974)Google Scholar
  12. [49]
    K.J. Rawson, N.C Tupper, Basic Ship Theory (Elsevier Butterworth-Heinemann, 2001)Google Scholar
  13. [55]
    A. Romano, Classical Mechanics with Mathematica (Birkhäser Basel, 2012)Google Scholar
  14. [59]
    N. Salvesen, E.O. Tuck, O. Faltinsen, Ship motions and sea loads. Trans. Soc. Naval Architects Marine Eng. 78, (1970)Google Scholar
  15. [70]
    Y. Yang, C. Zhou, X. Jia, Robust adaptive fuzzy control and its application to ship roll stabilization. Inform. Sci. 142, (2002)Google Scholar
  16. [71]
    I.R. Young, Wind Generated Ocean Waves (Elsevier New York, 1999)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Antonio Romano
    • 1
  • Addolorata Marasco
    • 1
  1. 1.Department of Mathematics and Applications “R. Caccioppoli”University of Naples Federico IINaplesItaly

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