| 时间尺度上二阶Lagrange系统Noether对称性与守恒量 |
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| 引用本文： | 赵淑琼,朱建青.时间尺度上二阶Lagrange系统Noether对称性与守恒量[J].华中师范大学学报(自然科学版),2021,55(1):30-35. |
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| 作者姓名： | 赵淑琼 朱建青 |
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| 作者单位： | 苏州科技大学数理学院,江苏苏州215009;苏州科技大学数理学院,江苏苏州215009 |
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| 基金项目： | 国家自然科学基金;国家自然科学基金;江苏省自然科学基金 |
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| 摘 要： | 研究了时间尺度上二阶Lagrange系统Noether对称性与守恒量， 以时间尺度上二阶Lagrange系统的运动方程为基础， 基于Hamilton作用量在无限小群变换下的不变性原理， 给出了时间尺度上二阶Lagrange系统的广义Noether对称变换以及广义Noether准对称变换下的定义与判据， 得出了无限小变换下Noether定理， 最后举例说明结果的应用.
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| 关 键 词： | 时间尺度 Lagrange系统 Noether对称性 守恒量 |
| 收稿时间： | 2021-01-13 |
Noether theorem of second-order Lagrange systems on time scales |
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| ZHAO Shuqiong,ZHU Jianqing.Noether theorem of second-order Lagrange systems on time scales[J].Journal of Central China Normal University(Natural Sciences),2021,55(1):30-35. |
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| Authors: | ZHAO Shuqiong ZHU Jianqing |
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| Institution: | College of Mathematics and Physics， Suzhou University of Science and Technology， Suzhou， Jiangsu 215009， China |
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| Abstract: | The Noether symmetry and conserved quantity of the second-order Lagrange system on time scales are studied in this paper. The equations corresponding to the second-order Lagrange system on time scales are introduced. Then based on the principle of invariance of Hamilton interaction under infinite small group transformation， the generalized Noether symmetric transformation of the second-order Lagrange system and the definition and criteria under the generalized Noether quasi-symmetric transformation are studied. The Noether theorems under the general infinitesimal transformation are obtained. An example is given to illustrate the application of the theorem. |
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| Keywords: | time scales Lagrange system Noether symmetry conserved quantity |
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