Skip to main content

Melnikov’s Method for Ship Motions without the Constraint of Small Linear Damping

  • Conference paper
  • 1380 Accesses

Part of the book series: Iutam Bookseries ((IUTAMBOOK,volume 8))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chen SL, Shaw SW, and Troesch AW(1999): A Systematic Approach to Modelling Nonlinear Multi-DOF Ship Motions in Regular Seas, J of Ship Research 43:25–37

    Google Scholar 

  2. Endo T, Chua LO, and Narita T (1989):Chaos From Phase-Locked Loops–Part II: High Dissipation Case, IEEE Tran Circuits Sys 36:255–263

    Article  MathSciNet  Google Scholar 

  3. Falzarano JM (1990) Predicting complicated dynamics leading to vessel capsizing. PhD Thesis, University of Michigan, Ann Arbor

    Google Scholar 

  4. Falzarano JM, Shaw SW, and Troesch AW (1992): Application of global methods for analyzing dynamical systems to ship rolling motion and capsizing, Int J of Bifurcation and Chaos 1:101–115

    Article  MathSciNet  Google Scholar 

  5. Jiang C, Troesh AW, and Shaw SW (2000): Capsize criteria for ship models with memory-dependent hydrodynamics and random excitation, Phil Trans R Soc Lond A358:1761-1791

    Article  MATH  Google Scholar 

  6. Nayfeh AH, Balachandran B (1995):Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, Wiley, New York

    MATH  Google Scholar 

  7. Salam FM (1987) The Melnikov technique for highly dissipative systems. SIAM J Appl Math 47:232–243

    Article  MATH  MathSciNet  Google Scholar 

  8. Simiu E (2002) Chaotic Transitions in Deterministic and Stochastic Dynamical Systems: Application of Melnikov Processes in Engineering, Physics, and Neuroscience, Princeton University Press

    Google Scholar 

  9. Spyrou KJ, Cotton B, and Gurd B (2002): Analytical Expressions of Capsize Boundary for a Ship with Roll Bias in Beam Waves, J of Ship Research 46:167–174

    Google Scholar 

  10. Thompson JMT, Bishop SR, and Leung LM (1987): Fractal basins and chaotic bifurcations prior to escape from a potential well, Physics Letters A 121:116–120

    MathSciNet  Google Scholar 

  11. Thompson JMT (1997): Designing against capsize in beam seas: Recent advances and new insights, Appl Mech Rev 50:307-325

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media B.V.

About this paper

Cite this paper

Wu*, W., McCue†, L. (2008). Melnikov’s Method for Ship Motions without the Constraint of Small Linear Damping. In: Kreuzer, E. (eds) IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering. Iutam Bookseries, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8630-4_26

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-8630-4_26

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8629-8

  • Online ISBN: 978-1-4020-8630-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics