Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
- 3.
It is evident that this hypothesis can be accepted for a big ship since, if the goods are well packed in the hold, any position change of passengers does not modify the mass distribution. This in not true for a small barge in which, any position change of a passenger should modify the mass distribution.
- 4.
All the definitions and notations used in this chapter are the same used in [55], Chapters 12, 15, 16.
- 5.
It is evident that, composing these three rotations, we obtain a Cartesian frame fixed in the body. It is possible to prove that, given any transformation \(G\xi \eta \zeta \rightarrow Gx^{{\prime}}y^{{\prime}}z^{{\prime}}\) by an orthogonal matrix, it is possible to determine \(\varphi\), θ, and ψ.
- 6.
- 7.
- 8.
It can be proved that \(\overline{\mathbf{K}}\) does not depend on the choice of the pole.
- 9.
See, [71], pg. 5.
- 10.
It can be proved that this circumstance is verified if the amplitude K 1 in (13.78) is such that K 1 ≪ λ.
References
R. Bhattacharrya, Dynamics of marine vehicles (Wiley, New York, 1978)
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)
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)
F. John, On the motion of floating bodies - Part I. Comm. Pure Appl. Math. 2, (1949)
F. John, On the motion of floating bodies - Part II. Comm. Pure Appl. Math. 3, (1950)
R. Nabergoj, Fondamenti di tenuta della nave al mare (Notes Trieste, 2010)
J.N. Newman, Theory of ship motions. Adv. Appl. Mech. 18, (1978)
J.R. Paulling, R.M. Rosenberg, On unstable ship motions resulting from nonlinear coupling. J. Ship Res. 3, (1959)
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)
T. Perez, Ship Motion Control: Course Keeping and Roll Stabilisation Using Rudder and Fins (Springer-Verlag London, 2005)
W.G. Price, R.E.D. Bishop, Probabilistic Theory of Ship Dynamics (Chapman and Hall, London, 1974)
K.J. Rawson, N.C Tupper, Basic Ship Theory (Elsevier Butterworth-Heinemann, 2001)
A. Romano, Classical Mechanics with MathematicaⓇ (Birkhäser Basel, 2012)
N. Salvesen, E.O. Tuck, O. Faltinsen, Ship motions and sea loads. Trans. Soc. Naval Architects Marine Eng. 78, (1970)
Y. Yang, C. Zhou, X. Jia, Robust adaptive fuzzy control and its application to ship roll stabilization. Inform. Sci. 142, (2002)
I.R. Young, Wind Generated Ocean Waves (Elsevier New York, 1999)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Romano, A., Marasco, A. (2014). Fluid Dynamics and Ship Motion. In: Continuum Mechanics using Mathematica®. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-1604-7_13
Download citation
DOI: https://doi.org/10.1007/978-1-4939-1604-7_13
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4939-1603-0
Online ISBN: 978-1-4939-1604-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)