| 相空间中非完整力学系统的对称性与非Noether守恒量 |
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| 引用本文： | 张毅,尚玫. 相空间中非完整力学系统的对称性与非Noether守恒量[J]. 苏州科技学院学报(自然科学版), 2007, 24(1): 1-8 |
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| 作者姓名： | 张毅 尚玫 |
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| 作者单位： | 1. 苏州科技学院,土木工程系,江苏,苏州,215011
2. 北京理工大学,理学院,北京,100081 |
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| 基金项目： | 江苏省高校自然科学基金;江苏省教育厅青蓝工程项目 |
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| 摘 要： | 在增广相空间中研究非完整约束力学系统的对称性与守恒量。建立了系统的运动微分方程；给出了系统的Noether对称性、Lie对称性和Mei对称性的判据；研究了三种对称性之间的关系；得到了相空间中非完整约束力学系统的两类非Noether守恒量——Hojman守恒量和Mei守恒量，研究了对称性和守恒量之间的内在关系。文末，举例说明结果的应用。
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| 关 键 词： | 分析力学 非完整约束 对称性 守恒量 相空间 |
| 文章编号： | 1672-0687(2007)01-0001-08 |
| 修稿时间： | 2006-08-16 |
Non-Noether Conserved Quantities of Mechanical Systems with Nonholonomic Constraints in Phase Space |
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| ZHANG Yi,SHANG Mei. Non-Noether Conserved Quantities of Mechanical Systems with Nonholonomic Constraints in Phase Space[J]. Journal of University of Science and Technology of Suzhou, 2007, 24(1): 1-8 |
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| Authors: | ZHANG Yi SHANG Mei |
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| Affiliation: | 1.Dept. of Civil Engineering, USTS, Suzhou 215011, China;2. School of Science, Beijing Institute of Technolo- gy, Beijing 100081, China |
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| Abstract: | This paper studies the symmetries and conserved quantities of mechanical systems with northolonomic constraints in extended phase space. The systematic differential equations of motion are established. The criteria for Noether symmetry, Lie symmetry and Mei symmetry are given, and the relations among three symmetries are researched. Two types of new non-Noether conserved quantities- Hojman quantity and Mei quantity,for the mechanical systems with nonholonomic constraints in phase space are obtained, and the intrinsic relations between symmetries and conserved quantities are explored. At the end of this paper, an example is given to illustrate the application of the results. |
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| Keywords: | analytical mechanics non-holonomic constraint symmetry, conserved quantity phase space |
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