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Regular and chaotic motion of two bodies swinging on a rod

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  • Lazare Osmanov

    (Free University of Tbilisi)

  • Ramaz Khomeriki

    (Ivane Javakhishvili Tbilisi State University)

Abstract

We investigate regular and chaotic dynamics of two bodies swinging on a rod, which differs from all the other mechanical analogies: depending on initial conditions, its oscillation could end very quickly and the reason is not a drag force or energy loss. We use various tools to analyze motion, such as Poincaré section for quasi-periodic and chaotic cases. We calculate Lyapunov characteristic exponent by different methods including Finite Time Lyapunov Exponent analysis. Our calculations show that the maximal Lyapunov exponent is always positive except in the marginal cases when one observes quasi-periodic oscillations. Graphic abstract

Suggested Citation

  • Lazare Osmanov & Ramaz Khomeriki, 2022. "Regular and chaotic motion of two bodies swinging on a rod," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(11), pages 1-7, November.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:11:d:10.1140_epjb_s10051-022-00435-5
    DOI: 10.1140/epjb/s10051-022-00435-5
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    References listed on IDEAS

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    1. Gaspard, Pierre, 1997. "Chaos and hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(1), pages 54-67.
    2. Stachowiak, Tomasz & Okada, Toshio, 2006. "A numerical analysis of chaos in the double pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 417-422.
    3. Manchein, C. & Beims, M.W. & Rost, J.M., 2014. "Characterizing weak chaos in nonintegrable Hamiltonian systems: The fundamental role of stickiness and initial conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 186-193.
    4. Sabarathinam, S. & Thamilmaran, K., 2015. "Transient chaos in a globally coupled system of nearly conservative Hamiltonian Duffing oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 129-140.
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