| Mathews⁃Lakshmanan 振子方程的分析力学解法 |
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| 引用本文： | 李京颍,丁光涛. Mathews⁃Lakshmanan 振子方程的分析力学解法[J]. 动力学与控制学报, 2018, 16(1): 1-5. DOI: 10.6052/1672-6553-2017-66 |
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| 作者姓名： | 李京颍 丁光涛 |
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| 作者单位： | 1. 阜阳师范学院物理与电子科学学院,阜阳,236032;2. 安徽师范大学物理与电子信息学院,芜湖,241000 |
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| 基金项目： | 国家自然科学基金资助项目(11472063) |
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| 摘 要： | 本文以求解非线性非保守的Mathews-Lakshmanan振子(以下简写成M-L振子)为例,说明分析力学理论和方法在非线性系统研究中的应用.根据变分法逆问题理论,将M-L振子方程变换为自伴随形式方程;利用四种方法构造出振子的拉格朗日函数和哈密顿函数;分别基于诺特理论和哈密顿-雅可比方法得到M-L振子方程的解.
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| 关 键 词： | Mathews-Lakshmanan振子 变分法逆问题 非线性 分析力学 Mathews-Lakshmanan oscillator inverse problem of variational calculus nonlinearity analytical mechanics |
| 收稿时间： | 2016-05-15 |
| 修稿时间： | 2016-09-25 |
ANALYTICAL MECHANICS METHODS FOR SOLVING MATHEWS-LAKSHMANAN OSCILLATOR |
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| Li Jingying and Ding Guangtao. ANALYTICAL MECHANICS METHODS FOR SOLVING MATHEWS-LAKSHMANAN OSCILLATOR[J]. Journal of Dynamics and Control, 2018, 16(1): 1-5. DOI: 10.6052/1672-6553-2017-66 |
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| Authors: | Li Jingying and Ding Guangtao |
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| Affiliation: | 1.College of Physics and Electronic Science, Fuyang Normal College, Fuyang236032;2.College of Physics and Electronic Information, Anhui Normal University, Wuhu241000; |
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| Abstract: | The solving of non-conservative and non-linear Mathews-Lakshmanan oscillator is taken as an example to illustrate the application of the theories and methods of analytical mechanics in studying the non-linear systems.According to the theories of inverse problem of variational calculus,the equation of M-L oscillator is transformed into a self-adjoint equation.The Lagrangian and Hamiltonian of M-L oscillator are also constructed by four methods.Eventually,the equation of M-L oscillator is solved based on the Noether theory and the Hamilton-Jacobi method,respectively. |
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| Keywords: | Analytical mechanics Inverse problem of variational calculus Mathews-Lakshmanan oscillator Nonlinearity |
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