| 变质量完整力学系统的形式不变性与非Noether守恒量 |
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| 引用本文： | 梅凤翔. 变质量完整力学系统的形式不变性与非Noether守恒量[J]. 北京理工大学学报, 2003, 23(1): 1-3 |
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| 作者姓名： | 梅凤翔 |
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| 作者单位： | 北京理工大学,理学院力学系,北京,100081 |
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| 基金项目： | 国家自然科学基金;19972010,10272021; |
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| 摘 要： | 利用时间不变的特殊无限小变换下的形式不变性，研究变质量完整力学系统的非Noether守恒量，建立系统的运动微分方程，研究特殊无限小变换下系统形式不变性的定义和判据，给出形式不变性为Lie对称性的充要条件，得到形式不变性导致非Noether守恒量的条件以及守恒量的形式，举例说明结果的应用。
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| 关 键 词： | 变质量完整力学系统 非Noether守恒量 分析力学 形式不变性 特殊无限小变换 Lie对称性 |
| 文章编号： | 1001-0645(2003)01-0001-03 |
| 收稿时间： | 2002-10-07 |
| 修稿时间： | 2002-10-07 |
Form Invariance and Non-Noether Conserved Quantity for Holonomic Mechanical Systems with Variable Mass |
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| MEI Feng-xiang. Form Invariance and Non-Noether Conserved Quantity for Holonomic Mechanical Systems with Variable Mass[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 2003, 23(1): 1-3 |
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| Authors: | MEI Feng-xiang |
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| Affiliation: | Department.of Mechanics, School of Science, Beijing Institute of Technology, Beijing100081, China |
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| Abstract: | Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the holonomic mechanical systems with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the systems under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether conserved quantity and the form of the conserved quantity are obtained. |
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| Keywords: | analytical mechanics variable mass system form invariance conserved quantity |
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