共查询到17条相似文献,搜索用时 109 毫秒
1.
研究了非完整力学系统的一种新对称性——Noether-Lie对称性及其守恒量. 给出了非完整力学系统Noether -Lie对称性的定义和判据,提出系统的Noether-Lie对称性导致Noether守恒量和广义Hojman守恒量的定理. 举例说明了结果的应用. Hojman守恒量是所给出的广义Hojman守恒量的特例.
关键词:
非完整力学系统
Noether-Lie对称性
Noether守恒量
广义Hojman守恒量 相似文献
2.
在群的无限小变化下, 研究奇异变质量单面非完整系统Nielsen方程的Noether-Lie对称性. 建立系统运动微分方程的Nielsen形式, 给出系统Nielsen方程的Noether-Lie对称性的定义、判据和命题, 得到系统Nielsen 方程的Noether-Lie对称性所导致的Noether守恒量和广义Hojman守恒量. 最后给出说明性算例说明结果的应用.
关键词:
奇异变质量系统
单面非完整约束
Nielsen方程
Noether-Lie对称性 相似文献
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研究非完整力学系统的Noether对称性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下,给出系统的特殊Noether对称性与守恒量,并给出特殊Noether对称性导致特殊Lie对称性的条件. 由系统的特殊Noether对称性,得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出一个例子说明本结果的应用
关键词:
分析力学
非完整系统
Noether对称性
非Noether守恒量
Hojman守恒量 相似文献
5.
采用变劲度系数的耦合弹簧构建一实际的两自由度弱非线性耦合系统, 用近似Lie对称性理论研究系统的一阶近似Lie对称性与近似守恒量, 得到6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1个一阶近似守恒量为稳定的一阶近似守恒量.
关键词:
两自由度弱非线性耦合系统
近似Lie对称性
近似守恒量 相似文献
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在增广相空间中研究单面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Norther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;得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量,研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用.
关键词:
分析力学
单面约束
对称性
守恒量
相空间 相似文献
10.
研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程;给出了系统的Lie对称性和Mei对称性的定义和判据;对于单面非Chetaev型非完整系统,证明了在一定条件下,由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量,由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量;研究了对称性和新守恒量之间的相互关系.文末,举例说明结果的应用.
关键词:
分析力学
单面约束
非完整系统
对称性
Hojman守恒量
Mei守恒量 相似文献
11.
ZHANG Xiao-Ni FANG Jian-Hui WANG Peng DING Ning 《理论物理通讯》2008,49(2):305-307
In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results. 相似文献
12.
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry. 相似文献
13.
ZHANG Xiao-Ni FANG Jian-Hui PANG Ting LIN Peng 《理论物理通讯》2009,51(2):205-208
For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied. The criterion equation of the Noether symmetry for the system is got. The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained. Finally, an example is given to illustrate the application of the results. 相似文献
14.
XIA Li-Li LI Yuan-Cheng WANG Jing HOU Qi-Bao 《理论物理通讯》2006,46(3):415-418
This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result. 相似文献
15.
This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result. 相似文献
16.
Based on the total time derivative along the trajectory of the
time, we study the unified symmetry of Vacco dynamical systems.
The definition and the criterion of the unified symmetry for the
system are given. Three kinds of conserved quantities, i.e. the
Noether conserved quantity, the generalized Hojman conserved
quantity and the Mei conserved quantity, are deduced from the
unified symmetry. An example is presented to illustrate the
results. 相似文献