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Analytical solution for the motion of a pendulum with rolling wheel: stability analysis

The current work focuses on the motion of a simple pendulum connected to a wheel and a lightweight spring. The fundamental equation of motion is transformed into a complicated nonlinear ordinary differential equation under restricted surroundings. To achieve the approximate regular solution, the com...

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Detalles Bibliográficos
Autores principales: Moatimid, Galal M., Amer, T. S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9309161/
https://www.ncbi.nlm.nih.gov/pubmed/35871675
http://dx.doi.org/10.1038/s41598-022-15121-w
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author Moatimid, Galal M.
Amer, T. S.
author_facet Moatimid, Galal M.
Amer, T. S.
author_sort Moatimid, Galal M.
collection PubMed
description The current work focuses on the motion of a simple pendulum connected to a wheel and a lightweight spring. The fundamental equation of motion is transformed into a complicated nonlinear ordinary differential equation under restricted surroundings. To achieve the approximate regular solution, the combination of the Homotopy perturbation method (HPM) and Laplace transforms is adopted in combination with the nonlinear expanded frequency. In order to verify the achievable solution, the technique of Runge–Kutta of fourth-order (RK4) is employed. The existence of the obtained solutions over the time, as well as their related phase plane plots, are graphed to display the influence of the parameters on the motion behavior. Additionally, the linearized stability analysis is validated to understand the stability in the neighborhood of the fixed points. The phase portraits near the equilibrium points are sketched.
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spelling pubmed-93091612022-07-26 Analytical solution for the motion of a pendulum with rolling wheel: stability analysis Moatimid, Galal M. Amer, T. S. Sci Rep Article The current work focuses on the motion of a simple pendulum connected to a wheel and a lightweight spring. The fundamental equation of motion is transformed into a complicated nonlinear ordinary differential equation under restricted surroundings. To achieve the approximate regular solution, the combination of the Homotopy perturbation method (HPM) and Laplace transforms is adopted in combination with the nonlinear expanded frequency. In order to verify the achievable solution, the technique of Runge–Kutta of fourth-order (RK4) is employed. The existence of the obtained solutions over the time, as well as their related phase plane plots, are graphed to display the influence of the parameters on the motion behavior. Additionally, the linearized stability analysis is validated to understand the stability in the neighborhood of the fixed points. The phase portraits near the equilibrium points are sketched. Nature Publishing Group UK 2022-07-24 /pmc/articles/PMC9309161/ /pubmed/35871675 http://dx.doi.org/10.1038/s41598-022-15121-w Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Moatimid, Galal M.
Amer, T. S.
Analytical solution for the motion of a pendulum with rolling wheel: stability analysis
title Analytical solution for the motion of a pendulum with rolling wheel: stability analysis
title_full Analytical solution for the motion of a pendulum with rolling wheel: stability analysis
title_fullStr Analytical solution for the motion of a pendulum with rolling wheel: stability analysis
title_full_unstemmed Analytical solution for the motion of a pendulum with rolling wheel: stability analysis
title_short Analytical solution for the motion of a pendulum with rolling wheel: stability analysis
title_sort analytical solution for the motion of a pendulum with rolling wheel: stability analysis
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9309161/
https://www.ncbi.nlm.nih.gov/pubmed/35871675
http://dx.doi.org/10.1038/s41598-022-15121-w
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