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Open AccessArticle

Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation

1
Student of the International Faculty of Engineering, Lodz University of Technology, 36 Żwirki Str., 90-001 Lodz, Poland
2
Department of Automation, Biomechanics and Mechatronics, Faculty of Mechanical Engineering, Lodz University of Technology, 1/15 Stefanowskiego Str., 90-924 Lodz, Poland
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(4), 90; https://doi.org/10.3390/mca24040090
Received: 23 September 2019 / Revised: 14 October 2019 / Accepted: 15 October 2019 / Published: 16 October 2019
This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions. View Full-Text
Keywords: parametric pendulum; Lyapunov exponents; quasi-periodic behavior; Chaos parametric pendulum; Lyapunov exponents; quasi-periodic behavior; Chaos
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Śmiechowicz, W.; Loup, T.; Olejnik, P. Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation. Math. Comput. Appl. 2019, 24, 90.

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