Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems
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 recogn...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/14/3159 |
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| author | A. I. Ismail T. S. Amer W. S. Amer |
| author_facet | A. I. Ismail T. S. Amer W. S. Amer |
| author_sort | A. I. Ismail |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T00:51:54Z |
| format | Article |
| id | doaj.art-8f78b5f31be549c28a2fd07b237d3b80 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:51:54Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8f78b5f31be549c28a2fd07b237d3b802023-11-18T20:21:27ZengMDPI AGMathematics2227-73902023-07-011114315910.3390/math11143159Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical SystemsA. I. Ismail0T. S. Amer1W. S. Amer2Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, Makkah 5555, Saudi ArabiaMathematics Department, Faculty of Science, Tanta University, Tanta 31527, EgyptMathematics and Computer Science Department, Faculty of Science, Menoufia University, Shibin El-Kom 32511, EgyptThis 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.https://www.mdpi.com/2227-7390/11/14/3159nonlinear dynamicsperturbation methodsdynamical systemperiodic solutions of rigid bodiessatellite motionsnavigation |
| spellingShingle | A. I. Ismail T. S. Amer W. S. Amer Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems Mathematics nonlinear dynamics perturbation methods dynamical system periodic solutions of rigid bodies satellite motions navigation |
| title | Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems |
| title_full | Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems |
| title_fullStr | Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems |
| title_full_unstemmed | Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems |
| title_short | Modification of the Large Parameter Approach for the Periodic Solutions of Nonlinear Dynamical Systems |
| title_sort | modification of the large parameter approach for the periodic solutions of nonlinear dynamical systems |
| topic | nonlinear dynamics perturbation methods dynamical system periodic solutions of rigid bodies satellite motions navigation |
| url | https://www.mdpi.com/2227-7390/11/14/3159 |
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