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Bifurcation and Chaos of Multi-body Dynamical Systems

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Vibration Problems ICOVP 2011

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 139))

Abstract

Triple physical pendulum in a form of three connected rods with the first link subjected to an action of constant torque and with a horizontal barrier is used as an example of plane mechanical system with rigid limiters of motion. Special transition rules for solutions of linearized equations at impact instances (Aizerman-Gantmakher theory) are used in order to apply classical tools for Lyapunov exponents computation as well as for stability analysis of periodic orbits (used in seeking for stable and unstable periodic orbits and bifurcations of periodic solutions analysis). Few examples of extremely rich bifurcational dynamics of triple pendulum are presented.

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Acknowledgments

The work has been supported by the Ministry of Science and Higher Education under the grant no. 0040/B/T02/2010/38. J. Awrejcewicz acknowledges support of the Alexander von Humboldt Award.

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Authors and Affiliations

  1. LOEWE-Zentrum AdRIA, TU Darmstadt, Bartningstr. 53, 64289, Darmstadt, Germany

    Jan Awrejcewicz

  2. Department of Automation and Biomechanics, Technical University of Lodz, Lodz, Poland

    Jan Awrejcewicz & G. Kudra

Authors
  1. Jan Awrejcewicz
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  2. G. Kudra
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Corresponding author

Correspondence to Jan Awrejcewicz .

Editor information

Editors and Affiliations

  1. , Institute of Theoretical and Applied Mec, Academy of Sciences of the Czech Republi, Prosecka 76, Prague 9, 190 00, Czech Republic

    Jiří Náprstek

  2. , Institute of Thermomechanics, Academy of Sciences of the Czech Republi, Dolejskova 1402/5, Prague, 18200, Czech Republic

    Jaromír Horáček

  3. , Institute of Thermomechanics, Academy of Sciences of the Czech Republi, Dolejskova 1402/5, Prague, 18200, Czech Republic

    Miloslav Okrouhlík

  4. , Dept. of Engineering Mechanics, Technical University of Liberec, Studentska 2, Liberec, 46117, Czech Republic

    Bohdana Marvalová

  5. , Mathematisch Instituut, University of Utrecht, Budapestlaan 6, Utrecht, 3584 CD, Netherlands

    Ferdinand Verhulst

  6. , Center for Rotating Machinery Dynamics a, Cleveland State University, Euclid Avenue 2121SH 248, Cleveland, 44115-2214, Ohio, USA

    Jerzy T. Sawicki

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Awrejcewicz, J., Kudra, G. (2011). Bifurcation and Chaos of Multi-body Dynamical Systems. In: Náprstek, J., Horáček, J., Okrouhlík, M., Marvalová, B., Verhulst, F., Sawicki, J. (eds) Vibration Problems ICOVP 2011. Springer Proceedings in Physics, vol 139. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2069-5_1

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  • DOI: https://doi.org/10.1007/978-94-007-2069-5_1

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-2068-8

  • Online ISBN: 978-94-007-2069-5

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