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Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems

Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems

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References (49)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2020
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354720010104
Publisher site
See Article on Publisher Site

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.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Jan 20, 2020

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