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Regular and chaotic motion of two bodies swinging on a rod

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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.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

We would like to thank T. Gachechiladze, G. Bakhtadze, G. Khomeriki and M. Osmanov-Baisera for interesting discussions and valuable comments.

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Authors and Affiliations

  1. School of Physics, Free University of Tbilisi, David Aghmashenebeli Alley, 0159, Tbilisi, Georgia

    Lazare Osmanov

  2. Department of Physics, Ivane Javakhishvili Tbilisi State University, 3 Chavchavadze, 0128, Tbilisi, Georgia

    Ramaz Khomeriki

Authors
  1. Lazare Osmanov
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  2. Ramaz Khomeriki
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Contributions

LO contributed in setting general idea and implementation its numerical simulations as well as in writing manuscript draft. RK participated in choosing the methods for problem treatment and presentation of the simulation results as well as writing the paper draft.

Corresponding author

Correspondence to Lazare Osmanov.

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Osmanov, L., Khomeriki, R. Regular and chaotic motion of two bodies swinging on a rod. Eur. Phys. J. B 95, 182 (2022). https://doi.org/10.1140/epjb/s10051-022-00435-5

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  • DOI: https://doi.org/10.1140/epjb/s10051-022-00435-5

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