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# Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

by 1,*,
1
Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt
2
Institute of Applied Mechanics, Poznan University of Technology, 60-965 Poznan, Poland
3
Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta 31734, Egypt
*
Author to whom correspondence should be addressed.
Appl. Sci. 2021, 11(20), 9520; https://doi.org/10.3390/app11209520
Received: 18 September 2021 / Revised: 6 October 2021 / Accepted: 9 October 2021 / Published: 13 October 2021
This work looks at the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity. These pendulums have different lengths and are attached with different masses. Lagrange’s equations are employed to derive the governing kinematic system of motion. The multiple scales technique is utilized to find the desired approximate solutions up to the third order of approximation. Resonance cases have been classified, and modulation equations are formulated. Solvability requirements for the steady-state solutions are specified. The obtained solutions and resonance curves are represented graphically. The nonlinear stability approach is used to check the impact of the various parameters on the dynamical motion. The comparison between the attained analytic solutions and the numerical ones reveals a high degree of consistency between them and reflects an excellent accuracy of the used approach. The importance of the mentioned model points to its applications in a wide range of fields such as ships motion, swaying buildings, transportation devices and rotor dynamics. View Full-Text
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MDPI and ACS Style

Amer, T.S.; Starosta, R.; Elameer, A.S.; Bek, M.A. Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance. Appl. Sci. 2021, 11, 9520. https://doi.org/10.3390/app11209520

AMA Style

Amer TS, Starosta R, Elameer AS, Bek MA. Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance. Applied Sciences. 2021; 11(20):9520. https://doi.org/10.3390/app11209520

Chicago/Turabian Style

Amer, Tarek S., Roman Starosta, Abdelkarim S. Elameer, and Mohamed A. Bek. 2021. "Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance" Applied Sciences 11, no. 20: 9520. https://doi.org/10.3390/app11209520

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