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Nonlinear dynamics of triple pendulum with impacts

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Dynamics of a triple pendulum with damping, external forcing and impacts is analyzed numerically. In this mechanical system periodic, quasi-periodic and chaotic motions are detected. Specially developed numerical methods allow to track nonlinear behaviour of mechanical systems with many degrees of freedom and arbitrarily situated barriers, where an impact occurs.
Rocznik
Strony
97--112
Opis fizyczny
Bibliogr. 21 poz., rys., wykr.
Twórcy
  • Technical University of Łódź, Departament of Automatics and Biomechanics (K-16), ul. Stefanowskiego 1/15, 90-924 Łódź, Poland
autor
  • Technical University of Łódź, Departament of Automatics and Biomechanics (K-16), ul. Stefanowskiego 1/15, 90-924 Łódź, Poland
  • Ecole Nationale des Travaux Publics, De L’Etat / LGM / DGCB 1, Rue Audin. F69 518, Vaulx-En-Velin Cedex, France
Bibliografia
  • 1. W. Szemplińska-Stupnicka, The behaviour of nonlinear vibrating systems; vol. I - Fundamental Concepts and Methods: Applications to Single-Degree-of-Freedom Systems, Kluwer Academic Publishers Dordrecht 1990.
  • 2. E. Tyrkiel, W. Szemplińska-Stupnicka, A. Zubrzycki, On the boundary crises of chaotic attractors in nonlinear oscillators, Computer Assisted Mech. Engng. Sci., 7, 743-755, 2000.
  • 3. W. Szemplińska-Stupnicka, E. Tyrkiel, A. Zubrzycki, The global bifurcations that lead to transient tumbling chaos in a parametrically driven pendulum, Int. J. Bifurcation and Chaos, 10, 9, 2161-2175, 2000.
  • 4. W. Szemplińska-Stupnicka, E. Tyrkiel, A. Zubrzycki, On the stability “in the large” and unsafe initial disturbances in nonlinear oscillator, Computer Assisted Mech. Engng. Sci., 8, 155- 168, 2001.
  • 5. W. Szemplińska-Stupnicka, E. Tyrkiel, The oscillation-rotation attractors in a forced pendulum and their peculiar properties, to be published in Int. J. Bifurcation and Chaos, 2001.
  • 6. W. Szemplińska-Stupnicka, E. Tyrkiel, Common features of the onset of structurally stable chaos in nonlinear oscillators: a phenomenlogical approach, to be published in Nonlinear Dynamics, 2001.
  • 7. W. Szemplińska-Stupnicka, E. Tyrkiel, Bifurcations, chaos and fractals in pendulum dynamics, [in Polish], to be published.
  • 8. S.R. Bishop, M.J. Cliford, Zones of chaotic behavior in the parametrically excited pendulum, Journal of Sound and Vibrations 189, 1, 142-147, 1996.
  • 9. K. Yagasaki, Chaos in a pendulum with feedback control, Nonlinear Dynamics, 6, 125-142, 1994.
  • 10. A. C. Skeledon, Dynamics of a parametrically excited double pendulum, Physica D 75, 541-558, 1994.
  • 11. D. J. Acheson, T. Mullin, Upside down pendulums, Naturę, 366, 215-216, 1993.
  • 12. M. Kunze, Non-smooth dynamical systems, Lecture Notes in Mathematics 1744, Springer-Verlag, Berlin-Heidelberg 2000.
  • 13. B. Brogliato, Nonsmooth impact mechanics. Models, dynamics and control, Lecture Notes in Control and Information Sciences 220, Springer-Yerlag London 1996.
  • 14. J. Sygniewicz, Modelling of co-operation of the piston with piston rings and barrel [in Polish], Scientific Bulletin of Łódź Technical Unieversity 615/149, Łódź 1991.
  • 15. A. Wolf, B. Swift, H. Swinney, J. Vastano, Determining Lyapunov exponents from a time series, Physica 16D, 285-317, 1985.
  • 16. P. Müller, Calculation of Lyapunov exponents for dynamics systems with discontinuities, Chaos, Solitons and Fractals 5, 9, 1971-1681, 1995.
  • 17. J. Awrejcewicz, G. Kudra, Non-linear dynamics of a triple physical pendulum, [in:] Proceedings of the 2-nd Conference on “Methods and Computer Systems in the Scientific and Engineering Design Investigations”, R. Tadeusiewicz, S. Białas, T. Szmuc, M. Szymkat [Eds.], CCATIE, October 25-27, 231-236, Cracow 1999.
  • 18. J. Awrejcewicz, G. Kudra, Analysis of chaos in three coupled physical pendulums, [in:] Proceedings of the 5-th Conference on “Dynamical Systems Theory and Applications”, J. Awrejcewicz, J. Grabski, J. Mrozowski [Eds.], December 6-8, 121-124, Łódź 1999.
  • 19. J. Awrejcewicz, G. Kudra, Investigation of chaos in three coupled physical pendulums, [in:] Proceedings of the Third International Conference on Applied Mathematics and Engineering Sciences, CIMASP2000, Casablanca, Morocco, October 23-25, CD ROM, 6 pages.
  • 20. J. Awrejcewicz, G. Kudra, A family of coexisting regular and irregular Solutions in coupled three pendulums with impacts [in Polish], [in:] Proceedings of the 70 years birthday and 45 years of the scientific activity of Prof. Dr hab. Józef Giergiel and the 5-th School on Modal Analysis, December 12-14, 25-34, [Ed. T. Uhl], Kraków 2000.
  • 21. J. Awrejcewicz, G. Kudra., C.-H. Lamarque, Analysis of bifurcations and chaos in three coupled physical pendulums with impacts, [in:] Proceedings of Design Engineering Technical Conferences, Pittsburgh 2001.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0001-0090
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