共查询到17条相似文献,搜索用时 109 毫秒
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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
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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
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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
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Based on the concept of adiabatic invariant, the perturbation to Lie-Mei symmetry and adiabatic invariants for Birkhoffian systems are studied. The definition of the perturbation to Lie-Mei symmetry for the system is presented, and the criterion of the perturbation to Lie-Mei symmetry is given. Meanwhile, the Hojman adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained. 相似文献
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Noether-Mei Symmetry of Mechanical System in Phase Space 总被引:1,自引:0,他引:1
In this paper, a new kind of symmetry and its conserved
quantities of a mechanical system in phase space are studied.
The definition of this new symmetry, i.e., a Noether-Mei symmetry,
is presented, and the criterion of this symmetry is also given.
The Noether conserved quantity and the Mei conserved quantity
deduced from the Noether-Mei symmetry of the system are obtained.
Finally, two examples are given to illustrate the application of the results. 相似文献
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FANG Jian-Hui DING Ning WANG Peng 《理论物理通讯》2006,46(1):97-100
In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The defition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance. 相似文献
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FANG Jian-Hui 《理论物理通讯》2006,46(7)
In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance. 相似文献
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In this paper, a new kind of symmetry and its conserved quantities of a mechanical
system in phase space are studied. The definition of this new symmetry, i.e. a
Noether--Lie symmetry, is presented, and the criterion of this symmetry is also
given. The Noether conserved quantity and the generalized Hojman conserved quantity
of the Noether--Lie symmetry of the system are obtained. The Noether--Lie symmetry
contains the Noether symmetry and the Lie symmetry, and has more generalized
significance. 相似文献
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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
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Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanical system are studied. The definition and criterion of Noether-Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether-Mei symmetry of mechanical system can be obtained. 相似文献