Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems

A. I. Ismail, T. S. Amer () and W. S. Amer
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A. I. Ismail: Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah 5555, Saudi Arabia
T. S. Amer: Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt
W. S. Amer: Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shibin El-Kom 32511, Egypt

Mathematics, 2023, vol. 11, issue 14, 1-8

Abstract: This paper focuses on the modification of the large parameter approach (LPA), a novelty procedure, for estimating the periodic solutions of two degrees-of-freedom (DOF) autonomous quasi-linear systems with a first integral. This strategy is crucial because it provides an effective approach to recognizing approximate solutions to problems for which it is impossible to obtain exact solutions. These problems arise in the fields of physics, engineering, aerospace, and astronomy. They can be solved analytically using several perturbation approaches that depend on a small parameter that can be recognized according to the initial conditions and the body parameters of each problem. Therefore, we propose a large parameter instead of a small one to solve the aforementioned 2DOF systems, as well as provide a comparison between the suggested procedure and the previous approaches.

Keywords: nonlinear dynamics; perturbation methods; dynamical system; periodic solutions of rigid bodies; satellite motions; navigation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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