共查询到20条相似文献,搜索用时 31 毫秒
1.
Based on the infinitesimal and one parameter transformation,
the problem of Lie symmetry of three-order Lagrangian equations has
been studied. Under Lie transformation, the sufficient and necessary
condition which keeps three-order Lagrangian equations to be unchanged
and the invariant are obtained in this paper. 相似文献
2.
MA Shan-Jun YANG Xue-Hui YANG Rong 《理论物理通讯》2006,46(2):309-312
Based on the three-order Lagrangian equation, pseudo-Hamilton actoon I^* is defined and the three-order Hamilton's principle and the conditions are obtained in the paper. Then, the Noether symmetry about three-order Lagrangian equations is deduced. Finally, an example is given to illustrate the application of the result. 相似文献
3.
Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space 下载免费PDF全文
Hojman conserved quantities deduced from the special Lie symmetry,
the Noether symmetry and the form invariance for a nonholonomic
system of the unilateral non-Chetaev type in the event space are
investigated. The differential equations of motion of the system
above are established. The criteria of the Lie symmetry, the Noether
symmetry and the form invariance are given and the relations between
them are obtained. The Hojman conserved quantities are gained by
which the Hojman theorem is extended and applied to the nonholonomic
system of the unilateral non-Chetaev type in the event space. An
example is given to illustrate the application of the results. 相似文献
4.
Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems 下载免费PDF全文
In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results. 相似文献
5.
6.
This paper focuses on studying non-Noether conserved quantities of Lie
symmetry and of form invariance for a mechanical system in phase space
under the general infinitesimal transformation of groups. We obtain a new
non-Noether conserved quantity of Lie symmetry of the system, and Hojman and
Mei's results are of special cases of our conclusion. We find a
condition under which the form invariance of the system will lead to a Lie
symmetry, and, further, obtain a new non-Noether conserved quantity of form
invariance of the system. An example is given finally to illustrate these
results. 相似文献
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9.
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
10.
Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided.Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results. 相似文献
11.
Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space 下载免费PDF全文
This paper is devoted to studying the conformal invariance
and Noether symmetry and Lie symmetry of a holonomic mechanical
system in event space. The definition of the conformal invariance
and the corresponding conformal factors of the holonomic system in
event space are given. By investigating the relation between the
conformal invariance and the Noether symmetry and the Lie symmetry,
expressions of conformal factors of the system under these
circumstances are obtained, and the Noether conserved quantity and
the Hojman conserved quantity directly derived from the conformal
invariance are given. Two examples are given to illustrate the
application of the results. 相似文献
12.
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
13.
14.
15.
Using form invariance under special infinitesimal transformations
in which time is not variable, the non-Noether conserved quantity
of the relativistic nonholonomic system with variable mass is studied.
The differential equations of motion of the system are established.
The definition and criterion of the form invariance of
the system under 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.
Finally, an example is given to illustrate the application of the result. 相似文献
16.
研究非完整力学系统的形式不变性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下,给出非完整系统形式不变性的确定方程、约束限制方程和附加限制方程,提出并定义弱(强)形式不变性的概念. 研究特殊形式不变性导致特殊Lie对称性的条件,由系统的特殊形式不变性,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. 给出两个经典例子说明结果的应用.
关键词:
分析力学
非完整系统
形式不变性
非Noether守恒量
Hojman守恒量 相似文献
17.
This paper presents a form invariance of canonical equations for systems of generalized classical mechanics. Ac-cording to the invariance of the form of differential equations of motion under the infinitesimal transformations, this paper gives the definition and criterion of the form invariance for generalized classical mechanical systems, and estab-lishes relations between form invariance, Noether symmetry and Lie symmetry. At the end of the paper, an example is giver to illustrate the application of the results. 相似文献
18.
In this paper,we study the relation between the form invariance and Lie symmetry of non-holonomic systems.Firstly,we give the definitions and criteria of the form invariance and Lie symmetry in the systems.Next,their relation is deduced.We show that the structure equation and conserved quantity of the form invariance and Lie symmetry of non-holonomic systems have the same form.Finally,we give an example to illustrate the application of the result. 相似文献
19.
For a relativistic Birkhoman system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhottian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. An example is given to illustrate the application of the results. 相似文献
20.
XU Zhi-Xin 《理论物理通讯》2005,44(7)
For a relativistic Birkhoffian system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhoffian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. An example is given to illustrate the application of the results. 相似文献