| 从运动方程构造Lagrange函数的直接方法 |
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| 引用本文： | 丁光涛.从运动方程构造Lagrange函数的直接方法[J].动力学与控制学报,2010,8(4):305-310. |
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| 作者姓名： | 丁光涛 |
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| 作者单位： | 安徽师范大学物理与电子信息学院,芜湖,241000 |
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| 摘 要： | 根据对Lagrange函数的结构分析,提出直接从运动微分方程构造一维系统Lagrange函数新的一般方法和6种特殊方法.利用提出的方法导出若干运动微分方程的Lagrange函数.直接构造法证实一个系统具有多个不同而等效的Lagrange函数,甚至是Lagrange函数族.这种直接构造法也是构造Lagrange对称性并导出对应守恒量的一种途径.
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| 关 键 词： | Lagrange力学 逆问题 非保守系统 Lagrange对称性 |
| 收稿时间： | 2010/6/19 0:00:00 |
| 修稿时间： | 7/8/2010 12:00:00 AM |
A direct approach to the construction of Lagrangians form the motion equation |
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| Ding Guangtao.A direct approach to the construction of Lagrangians form the motion equation[J].Journal of Dynamics and Control,2010,8(4):305-310. |
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| Authors: | Ding Guangtao |
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| Affiliation: | Ding Guangtao(The College of Physics , Electronic Information,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | Based on the analysis of the structure of Lagrangions, a new general method and 6 special methods for the construction of Lagrangians for one dimensional system from the motion equation directly were presented. By use of the metthods, some Lagrangians of the differetial equations were derived. By means of the direct approach, it is verified that a system may have many different equivalent Lagrangians, even an infinite family of Lagrangians. The approach presented is a way to obtain Lagrange symmetries and the conserved quantities. |
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| Keywords: | Lagrange mechanics inverse problem non-conservative system Lagrange symmetry |
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