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Chaotic behaviour of a pendulum with variable length

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Il Nuovo Cimento B (1971-1996)

Summary

The Melnikov function for the prediction of Smale horseshoe chaos is applied to a driven damped pendulum with variable length. Depending on the parameters, it is shown that this dynamical system undertakes heteroclinic bifurcations which are the source of the unstable chaotic motion. The analytical results are illustrated by new numerical simulations. Furthermore, using the averaging theorem, the stability of the subharmonics is studied.

Riassunto

In questo articolo si applica la teoria di Melnikov per predire analiticamente la presenza di caos (Smale-horseshoe) in un pendolo con lunghezza variabile in presenza di dissipazione e di un termine forzante. Si mostra che tale sistema dinamico presenta una cascata di biforcazioni eterocliniche quando i parametri che entrano nell’equazione differenziale che lo descrive sono variati. La presenza di queste biforcazioni è la sorgente del moto caotico. Si studia inoltre la stabilità delle subarmoniche facendo uso del teorema della media temporale.

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Author notes

  1. M. Bartuccelli

    Present address: Mathematics Department, Queen Mary College University of London, Mile End Road, E1 4NS, London, England

Authors and Affiliations

  1. Laboratory of Applied Mathematical Physics, The Technical University of Denmark, DK-2800, Lyngby, Denmark

    M. Bartuccelli, P. L. Christiansen, V. Muto & M. P. Soerensen

  2. Physics Laboratory I, The Technical University of Denmark, DK-2800, Lyngby, Denmark

    N. F. Pedersen

Authors
  1. M. Bartuccelli
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  2. P. L. Christiansen
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  3. V. Muto
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  4. M. P. Soerensen
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  5. N. F. Pedersen
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Bartuccelli, M., Christiansen, P.L., Muto, V. et al. Chaotic behaviour of a pendulum with variable length. Nuov Cim B 100, 229–249 (1987). https://doi.org/10.1007/BF02722895

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  • DOI: https://doi.org/10.1007/BF02722895

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