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| Lagrange系统形式不变性和Lutzky守恒量 | |
| 引用本文： | 梅凤翔,许学军. Lagrange系统形式不变性和Lutzky守恒量[J]. 中国物理, 2005, 14(3): 449-451 |
| 作者姓名： | 梅凤翔 许学军 |
| 作者单位： | Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China;Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; Department of Physics, Zhejiang Normal University, Jinhua 321004, China |
| 基金项目： | Project supported by the National Natural Science Foundation of China (Grant No 10272021). |
| 摘 要： | 研究Lagrange系统形式不变性导致的Lutzky守恒量．给出Lagrange系统形式不变性的判据，得到了系统的形式不变性是Lie对称性的充分必要条件．利用Lutzky的结论[6]证明了Lagrange系统形式不变性能导致Lutzky守恒量．举例说明结果的应用． |
| 关 键 词： | 对称性；形式不变性；守恒量；Lagrange系统 |
| 收稿时间： | 2004-09-13 |
Form invariances and Lutzky conserved quantities for Lagrange systems |
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| Mei Feng-Xiang and Xu Xue-Jun. Form invariances and Lutzky conserved quantities for Lagrange systems[J]. Chinese Physics, 2005, 14(3): 449-451 | |
| Authors: | Mei Feng-Xiang and Xu Xue-Jun |
| Affiliation: | Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; Department of Physics, Zhejiang Normal University, Jinhua 321004, China |
| Abstract: | This paper focuses on studying a form invariance which can result in a Lutzky conserved quantity for a Lagrange system. The criterion of the form invariance for the system is given. The necessary and sufficient condition under which the form invariance is a Lie symmetry for the system is obtained. Lutzky's result is utilized to prove that the form invariance can lead to a Lutzky conserved quantity. Two examples are finally given to illustrate the application of the result. |
| Keywords: | symmetry form invariance conserved quantity Lagrange system |
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