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Nonlinear Dynamics

, Volume 36, Issue 2–4, pp 135–179 | Cite as

Stability and Capsizing of Ships in Random Sea – a Survey

  • Ludwig Arnold
  • Igor Chueshov
  • Gunter Ochs
Article

Abstract

This report is a survey of methods of stochastic and nonlinear dynamics in ship stability. After a brief introduction we describe the sea as a stationary random field. We then derive the general equations of motion of a ship from ‘first principles’, specializing to the case of the equations of motion for roll, heave and sway using strip theory from which eventually the ‘archetypal’ nonlinear random differential equation for the roll motion follows. This determines in particular how and where the stochasticity of the sea enters the equation. We then analyze simple nonlinear models of ship motion by means of the theory of random dynamical systems which amounts to studying invariant measures, Lyapunov exponents, random attractors and their (random) domain of attraction and to using stochastic bifurcation theory to describe qualitative changes.

Conley index random attractor random dynamical system random field random invariant set random seaway roll motion ship capsizing ship stability stochastic bifurcation stochastic stability 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ludwig Arnold
    • 1
  • Igor Chueshov
    • 2
  • Gunter Ochs
    • 1
  1. 1.Institut für Dynamische SystemeBremenGermany
  2. 2.Department of Mechanics and MathematicsKharkov UniversityKharkovUkraine

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