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研究Birkhoff系统规范变换对其Noether对称性、Lie对称性和Mei对称性的影响.在一定条件下,Noether对称性和守恒量不改变.Lie对称性和Hojaman守恒量仍保持不变.Mei对称性和新型守恒量可能变化,得到了Mei对称性和新型守恒量保持不变的条件.举例说明结果的应用.
关键词:
Birkhoff系统
规范变换
对称性
守恒量 相似文献
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研究一类动力学方程的Mei对称性的定义和判据,由Mei对称性通过Noether对称性可找到Noether守恒量.由Mei对称性通过Lie对称性可找到Hojman守恒量.同时,也可找到一类新型守恒量. 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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A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical
system, is presented. Under general infinitesimal transformations, the
determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable
mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the
corresponding holonomic mechanical system, the weak Hojman conserved
quantity and the strong Hojman conserved quantity of the nonholonomic controllable mechanical system are obtained. An example is given to illustrate the application of the results. 相似文献
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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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研究Lagrange系统的Mei对称性直接导致的一种守恒量. 给出系统的Mei对称性的定义和判据方程, 得到系统Mei对称性直接导致的一种守恒量的条件和形式,并举例说明结果的应用.
关键词:
Lagrange系统
Mei对称性
守恒量 相似文献
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The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange-Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results. 相似文献
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XU Xue-Jun QIN Mao-Chang MEI Feng-Xiang 《理论物理通讯》2005,44(11)
The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity,as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results. 相似文献
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Unified Symmetry of Hamilton Systems 总被引:1,自引:0,他引:1
XU Xue-Jun QIN Mao-Chang MEI Feng-Xiang 《理论物理通讯》2005,44(5):769-772
The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results. 相似文献
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Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints
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Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results. 相似文献
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DING Ning FANG Jian-Hui WANG Peng ZHANG Xiao-Ni 《理论物理通讯》2007,48(5):799-800
A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied. The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper. 相似文献
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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
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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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Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates
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The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results. 相似文献