共查询到20条相似文献,搜索用时 31 毫秒
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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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This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results. 相似文献
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For the holonomic nonconservative
system, by using the Noether symmetry, a non-Noether conserved quantity is
obtained directly under general infinitesimal transformations of groups in which time is variable. At first, the Noether symmetry, Lie symmetry, and
Noether conserved quantity are given. Secondly, the condition under which
the Noether symmetry is a Lie symmetry under general infinitesimal
transformations is obtained. Finally, a set of non-Noether conserved
quantities of the system are given by the Noether symmetry, and an example is
given to illustrate the application of the results. 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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研究Hamilton系统的形式不变性即Mei对称性,给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系,寻求系统的守恒量.给出一个例子说明本文结果的应用.
关键词:
Hamilton系统
Mei对称性
Noether对称性
Lie对称性
守恒量 相似文献
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Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper studies the Hojman conserved quantity, a non-Noether conserved quantity, deduced by special weak Noether symmetry for Lagrange systems. Under special infinitesimal transformations in which the time is not variable, its criterion is given and a method of how to seek the Hojman conserved quantity is presented. A Hojman conserved quantity can be found by using the special weak Noether symmetry. 相似文献
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Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales 下载免费PDF全文
This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians,namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton principle based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler–Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established.The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both classical and discrete cases are given. Finally, an example in Friedmann–Robertson–Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results. 相似文献
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The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass 下载免费PDF全文
This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results. 相似文献
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Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates 下载免费PDF全文
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
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Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod 下载免费PDF全文
In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables: time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals. 相似文献
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Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations 总被引:1,自引:0,他引:1 下载免费PDF全文
For a relativistic holonomic nonconservative system, by using the
Noether symmetry, a new non-Noether conserved quantity is given under
general infinitesimal transformations of groups. On the basis of the
theory of invariance of differential equations of motion under
general infinitesimal transformations, we construct the relativistic
Noether symmetry, Lie symmetry and the condition under which the
Noether symmetry is a Lie symmetry under general infinitesimal
transformations. By using the Noether symmetry, a new relativistic
non-Noether conserved quantity is given which only depends on the
variables $t$, $q_s $ and $\dot {q}_s $. An example is given to
illustrate the application of the results. 相似文献