The variational iteration method for a pendulum with a combined translational and rotational system

• Autorzy: Amir Muhammad , Ashraf Asifa , Haider Jamil Abbas

Identyfikatory

DOI

10.2478/ama-2024-0006

• Języki publikacji: EN

Abstrakty

EN

The dynamic analysis of complex mechanical systems often requires the application of advanced mathematical techniques. In this study, we present a variation iteration-based solution for a pendulum system coupled with a rolling wheel, forming a combined translational and rotational system. Furthermore, the Lagrange multiplier is calculated using the Elzaki transform. The system under investigation consists of a pendulum attached to a wheel that rolls without slipping on a horizontal surface. The coupled motion of the pendulum and the rolling wheel creates a complex system with both translational and rotational degrees of freedom. To solve the governing equations of motion, we employ the variation iteration method, a powerful numerical technique that combines the advantages of both variational principles and iteration schemes. The Lagrange multiplier plays a crucial role in incorporating the constraints of the system into the equations of motion. In this study, we determine the Lagrange multiplier using the Elzaki transform, which provides an effective means to calculate Lagrange multipliers for constrained mechanical systems. The proposed solution technique is applied to analyse the dynamics of a pendulum with a rolling wheel system. The effects of various system parameters, such as the pendulum length, wheel radius and initial conditions, are investigated to understand their influence on the system dynamics. The results demonstrate the effectiveness of the variation iteration method combined with the Elzaki transform in capturing the complex behaviour of a combined translational and rotational system. The proposed approach serves as a valuable tool for analysing and understanding the dynamics of similar mechanical systems encountered in various engineering applications.

Słowa kluczowe

EN

Elzaki transform; Variational iteration method; Combined translational and rotational system; Pendulum with rolling wheel

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2024
• Tom: Vol. 18, no. 1
• Strony: 48--54
• Opis fizyczny: Bibliogr. 47 poz., rys.

Twórcy

autor

Amir Muhammad

• Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan

• https://orcid.org/0009-0002-4871-4312

autor

Ashraf Asifa

• Department of Mathematics, University of Management and Technology, Lahore 54782, Pakistan

• https://orcid.org/0000-0002-7008-8576

autor

Haider Jamil Abbas

• Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan

• https://orcid.org/0009-0005-4786-7757

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