| 三阶Lagrange方程的Noether对称性、Mei对称性与守恒量 |
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| 引用本文： | 施勇,傅蓉,马善钧. 三阶Lagrange方程的Noether对称性、Mei对称性与守恒量[J]. 苏州科技学院学报(自然科学版), 2007, 24(4): 34-39 |
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| 作者姓名： | 施勇 傅蓉 马善钧 |
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| 作者单位： | 1. 江西师范大学,物理与通讯电子学院,江西,南昌,330027
2. 江西省宜春中学,江西,宜春,336000 |
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| 基金项目： | 江西省自然科学基金;江西省教育厅科研项目 |
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| 摘 要： | 讨论了不同力学系统的三阶Lagrange方程，给出了它们的Noether对称性判据和守恒量，研究了完整力学系统和完整有势力学系统三阶Lagrange方程的Mei对称性判据、结构方程和守恒量，分析了系统Noether对称性和Mei对称性的联系。并举例说明结果的应用。
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| 关 键 词： | 三阶Lagrange方程 加速度能 广义力变率 Noether对称性 Noether守恒量 Mei对称性 Mei守恒量 |
| 文章编号： | 1672-0687（2007）04-0034-06 |
| 收稿时间： | 2007-05-16 |
| 修稿时间： | 2007-05-16 |
Noether Symmetry, Mei Symmetry and Conserved Quantities of the Three-Order Lagrange Equations |
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| SHI Yong,FU Rong,MA Shan-jun. Noether Symmetry, Mei Symmetry and Conserved Quantities of the Three-Order Lagrange Equations[J]. Journal of University of Science and Technology of Suzhou, 2007, 24(4): 34-39 |
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| Authors: | SHI Yong FU Rong MA Shan-jun |
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| Abstract: | In this paper, the three-order Lagrange equations in different mechanical systems are discussed, and then the criteria of Noether symmetries and Noether conserved quantities for them are given. The criteria, structure equations and conserved quantities of Mei symmetry for three-order Lagrange equations are presented in both holonomic mechanic system and holonomic potential mechanic system. The relationship between Noether symmetry and Mei symmetry is also discussed. Finally, an example is given to illustrate the application of the resuit. |
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| Keywords: | three-order Lagrange equation energy of acceleration generalized force change rate Mei symmetry Mei conserved quantity Noether symmetry Noether conserved quantity |
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