The Transition to Chaos of Pendulum Systems
Source abstract
Abstract
We examine the nonlinear response of two planar pendula under external and kinematic excitations, which are very relevant as paradigmatic models in nonlinear dynamics. These pendula act under the action of an additional constant torque, and are subjected to one of the following excitations: a further external periodic torque, and a vertically periodic forcing of the point of suspension. Here, we show the influence of the constant torque strength on the transition to chaotic motions of the pendulum using both Melnikov analysis and the computation of the basins of attraction. The global bifurcations are illustrated by the erosion of the corresponding basins of attraction.
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Research context
OpenAlex topics: Chaos control and synchronization · Quantum chaos and dynamical systems · Elasticity and Wave Propagation
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Affiliations
Department of Automation, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland
Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland
Funding
the Polish Ministry of Science and Higher Education
References (33)
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