Anna Guerman
Convento de Sto. António. 6201-001 Covilhã, Portugal
Centre for Aerospace Science and Technologies, University of Beira Interior
Publications:
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Burov A., Guerman A., Nikonov V. I.
Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems
2020, vol. 25, no. 1, pp. 121-130
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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