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.
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.
Citation:
Alexander A. Burov, Anna D. Guerman, Vasily I. Nikonov, “Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems”, Regul. Chaotic Dyn., 25:1 (2020), 121–130
\Bibitem{BurGueNik20}
\by Alexander A. Burov, Anna D. Guerman, Vasily I. Nikonov
\paper Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 1
\pages 121--130
\mathnet{http://mi.mathnet.ru/rcd1053}
\crossref{https://doi.org/10.1134/S1560354720010104}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85079753102}
Linking options:
https://www.mathnet.ru/eng/rcd1053
https://www.mathnet.ru/eng/rcd/v25/i1/p121
This publication is cited in the following 2 articles:
Alexander A. Burov, Vasily I. Nikonov, “Dynamics of a heavy pendulum of variable length with a movable suspension point”, Acta Mech, 2024
Burov A.A., “Linear Invariant Relations in the Problem of the Motion of a Bundle of Two Bodies”, Dokl. Phys., 65:4 (2020), 147–148
Citation in format AMSBIB
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