The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator
The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) A...
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2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/2378989 |
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| author | Wang Guangbao Ding Guangtao |
| author_facet | Wang Guangbao Ding Guangtao |
| author_sort | Wang Guangbao |
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| description | The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. Therefore, the two-dimensional M-L oscillator is directly extended to the three-dimensional case, and it is proved that the three-dimensional M-L oscillator can be reduced to the two-dimensional case. (4) The two direct integration methods were provided to solve the two-dimensional M-L oscillator by using polar coordinate Lagrangian and pointed out that the one-dimensional M-L oscillator is a special case of the two-dimensional M-L oscillator. |
| format | Article |
| id | doaj-art-4af2429e321145b8a6aef8ea849706db |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-4af2429e321145b8a6aef8ea849706db2025-02-03T01:27:55ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/23789892378989The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan OscillatorWang Guangbao0Ding Guangtao1School of Media and Design, Chuzhou Polytechnic, No. 2188 Fengledadao, Chuzhou, Anhui 239000, ChinaSchool of Physics and Electronic Information, Anhui Normal University, Wuhu, Anhui 241000, ChinaThe purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. Therefore, the two-dimensional M-L oscillator is directly extended to the three-dimensional case, and it is proved that the three-dimensional M-L oscillator can be reduced to the two-dimensional case. (4) The two direct integration methods were provided to solve the two-dimensional M-L oscillator by using polar coordinate Lagrangian and pointed out that the one-dimensional M-L oscillator is a special case of the two-dimensional M-L oscillator.http://dx.doi.org/10.1155/2020/2378989 |
| spellingShingle | Wang Guangbao Ding Guangtao The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator Advances in Mathematical Physics |
| title | The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator |
| title_full | The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator |
| title_fullStr | The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator |
| title_full_unstemmed | The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator |
| title_short | The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator |
| title_sort | lagrangian and hamiltonian for the two dimensional mathews lakshmanan oscillator |
| url | http://dx.doi.org/10.1155/2020/2378989 |
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