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Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems

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Abstract

Invariant surfaces play a crucial role in the dynamics of mechanical systems separating regions filled with chaotic behavior. Cases where such surfaces can be found are rare enough. Perhaps the most famous of these is the so-called Hess case in the mechanics of a heavy rigid body with a fixed point.

We consider here the motion of a non-autonomous mechanical pendulum-like system with one degree of freedom. The conditions of existence for invariant surfaces of such a system corresponding to non-split separatrices are investigated. In the case where an invariant surface exists, combination of regular and chaotic behavior is studied analytically via the Poincaré-Mel’nikov separatrix splitting method, and numerically using the Poincaré maps.

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Funding

This research is partially supported by RFBR, grants 18-01-00335, project EMaDeS (Centro-01-0145-FEDER-000017), and the Portuguese Foundation for Science and Technologies via the Centre for Mechanical and Aerospace Science and Technologies, C-MAST, POCI-01-0145-FEDER-007718.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control”, Vavilova ul. 40, Moscow, 119333, Russia

    Alexander A. Burov & Vasily I. Nikonov

  2. National Research University “Higher School of Economics”, Myasnitskaya ul. 20, Moscow, 101000, Russia

    Alexander A. Burov & Vasily I. Nikonov

  3. Centre for Aerospace Science and Technologies, University of Beira Interior, Convento de Sto. António, 6201-001, Covilhã, Portugal

    Anna D. Guerman

Authors
  1. Alexander A. Burov
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  2. Anna D. Guerman
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  3. Vasily I. Nikonov
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Correspondence to Alexander A. Burov, Anna D. Guerman or Vasily I. Nikonov.

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The authors declare that they have no conflicts of interest.

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Burov, A.A., Guerman, A.D. & Nikonov, V.I. Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems. Regul. Chaot. Dyn. 25, 121–130 (2020). https://doi.org/10.1134/S1560354720010104

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