| 关于Mei对称性与Noether对称性的关系——以Lagrange系统为例 |
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| 引用本文： | 张毅. 关于Mei对称性与Noether对称性的关系——以Lagrange系统为例[J]. 力学与实践, 2016, 38(2): 169-171. doi: 10.6052/1000-0879-15-018 |
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| 作者姓名： | 张毅 |
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| 作者单位： | 苏州科技大学土木工程学院, 江苏 苏州 215011 |
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| 基金项目： | 国家自然科学基金资助项目(10972151 |
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| 摘 要： | 文章以Lagrange系统为例研究Mei对称性与Noether对称性之间的关系.基于无限小生成元向量作用下Lagrange函数的变分问题,建立了其Euler-Lagrange方程,研究了该变分问题的Noether对称性与守恒量.研究表明:该变分问题的Euler-Lagrange方程,Noether等式和Noether守恒量分别与Lagrange系统Mei对称性的判据方程,结构方程和Mei守恒量完全一致.文末以著名的Emden方程为例说明结果的应用.
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| 关 键 词： | Lagrange系统 Mei对称性 Noether对称性 变分问题 |
| 收稿时间： | 2016-01-21 |
THE RELATION BETWEEN THE MEI SYMMETRY AND THE NOETHER SYMMETRY-TAKING THE LAGRANGE SYSTEM AS AN EXAMPLE |
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| ZHANG Yi. THE RELATION BETWEEN THE MEI SYMMETRY AND THE NOETHER SYMMETRY-TAKING THE LAGRANGE SYSTEM AS AN EXAMPLE[J]. Mechanics in Engineering, 2016, 38(2): 169-171. doi: 10.6052/1000-0879-15-018 |
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| Authors: | ZHANG Yi |
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| Affiliation: | College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu, China |
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| Abstract: | This paper focuses on studying the relation between the Mei symmetry and the Noether symmetry, which takes the Lagrange system as an example. Based on the variational problem for Lagrangians under action of infinitesimal generator vectors, the Euler-Lagrange equations for the variational problem are established. The Noether symmetry for the variational problem is studied and corresponding conserved quantity is given. The studies show that the Euler-Lagrange equations and the Noether identity and the Noether conserved quantity of the variational problem are exactly the same with the criterion equation and structural equation and the conserved quantity for Mei symmetry of classical Lagrange system. In the end of the paper, we take the well-known Emden equation as example to illustrate the application of the results. |
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| Keywords: | Lagrange system Mei symmetry Noether symmetry variational problem |
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