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Article

Periodic Property and Instability of a Rotating Pendulum System

by
Ji-Huan He
1,2,3,*,
Tarek S. Amer
4,
Shimaa Elnaggar
5 and
Abdallah A. Galal
6
1
School of Science, Xi’an University of Architecture & Technology, Xi’an 710055, China
2
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
3
National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou 215000, China
4
Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt
5
Kafrelsheikh Higher Institute of Engineering and Technology, Kafrelsheikh 33511, Egypt
6
Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta 31734, Egypt
*
Author to whom correspondence should be addressed.
Axioms 2021, 10(3), 191; https://doi.org/10.3390/axioms10030191
Submission received: 12 July 2021 / Revised: 14 August 2021 / Accepted: 16 August 2021 / Published: 18 August 2021
(This article belongs to the Special Issue Dedicated to Professor Ji-Huan He on the Occasion of His 55th Birthday)
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Abstract

The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.
Keywords: homotopy method; nonlinear dynamics; lagrange’s equations; stability; variational principle homotopy method; nonlinear dynamics; lagrange’s equations; stability; variational principle

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MDPI and ACS Style

He, J.-H.; Amer, T.S.; Elnaggar, S.; Galal, A.A. Periodic Property and Instability of a Rotating Pendulum System. Axioms 2021, 10, 191. https://doi.org/10.3390/axioms10030191

AMA Style

He J-H, Amer TS, Elnaggar S, Galal AA. Periodic Property and Instability of a Rotating Pendulum System. Axioms. 2021; 10(3):191. https://doi.org/10.3390/axioms10030191

Chicago/Turabian Style

He, Ji-Huan, Tarek S. Amer, Shimaa Elnaggar, and Abdallah A. Galal. 2021. "Periodic Property and Instability of a Rotating Pendulum System" Axioms 10, no. 3: 191. https://doi.org/10.3390/axioms10030191

APA Style

He, J.-H., Amer, T. S., Elnaggar, S., & Galal, A. A. (2021). Periodic Property and Instability of a Rotating Pendulum System. Axioms, 10(3), 191. https://doi.org/10.3390/axioms10030191

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