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Jian-Le Cai 《International Journal of Theoretical Physics》2010,49(1):201-211
In this paper the definition of conformal invariance and determining equation for the holonomic system which correspond to
a nonholonomic system of Chetaev’s type are provided. Conformal factor expression is deduced through relationship between
a system’s conformal invariance and Lie symmetry. The necessary and sufficient condition that the system’s conformal invariance
would be Lie symmetry under transformations by the infinitesimal one-parameter transformation group is obtained. The conformal
invariance of weak and strong Lie symmetry for the nonholonomic system of Chetaev’s type is given using restriction equations
and additional restriction equations. And the system’s corresponding conserved quantity is derived with the aid of a structure
equation that gauge function satisfied. Lastly, an example is taken to illustrate the application of the result. 相似文献
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Conformal Invariance and Conserved Quantities of General Holonomic Systems 总被引:1,自引:0,他引:1 下载免费PDF全文
Conformed invariance and conserved quantities of general holonomic systems are studied. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators are described. The definition of conformal invariance and determining equation for the system are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and suttlcient condition, that conformal invariance of the system would be Lie symmetry, is obtained under the infinitesimal one-parameter transformation group. The corresponding conserved quantity is derived with the aid of a structure equation. Lastly, an example is given to demonstrate the application of the result. 相似文献
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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
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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
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Conformal invariance and conserved quantities of a general holonomic system with variable mass 下载免费PDF全文
Conformal invariance and conserved quantities of a general
holonomic system with variable mass are studied. The definition and
the determining equation of conformal invariance for a general
holonomic system with variable mass are provided. The conformal
factor expression is deduced from conformal invariance and Lie
symmetry. The relationship between the conformal invariance and the
Lie symmetry is discussed, and the necessary and sufficient
condition under which the conformal invariance would be the Lie
symmetry of the system under an infinitesimal one-parameter
transformation group is deduced. The conserved quantities of the
system are given. An example is given to illustrate the application
of the result. 相似文献
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研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用.
关键词:
Appell方程
Chetaev 型约束力学系统
Lie对称性
守恒量 相似文献
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This paper studies the conformal invariance and conserved quantities
of general holonomic systems in phase space. The definition and the
determining equation of conformal invariance for general holonomic
systems in phase space are provided. The conformal factor expression
is deduced from conformal invariance and Lie symmetry. The
relationship between the conformal invariance and the Lie symmetry
is discussed, and the necessary and sufficient condition that the
conformal invariance would be the Lie symmetry of the system under
the infinitesimal single-parameter transformation group is deduced.
The conserved quantities of the system are given. An example is
given to illustrate the application of the result. 相似文献
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Conformal invariance and a kind of Hojman conserved quantity of the Nambu system 总被引:1,自引:0,他引:1 下载免费PDF全文
Conformal invariance and a kind of Hojman conserved quantity of the Nambu system under infinitesimal transfor-mations are studied.The definition and the determining equation of conformal invariance of the system are presented.The necessary and sufficient condition under which the conformal invariance of the system would have Lie symmetry un-der infinitesimal transformations is derived.Then,the condition of existence and a kind of Hojman conserved quantity are obtained.Finally,an example is given to illustrate the application of the results. 相似文献
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Shao-Kai Luo Yun Dai Ming-Jing Yang Xiao-Tian Zhang 《International Journal of Theoretical Physics》2018,57(4):1024-1038
In this paper, we present a basic theory of fractional dynamics, i.e., the fractional conformal invariance of Mei symmetry, and find a new kind of conserved quantity led by fractional conformal invariance. For a dynamical system that can be transformed into fractional generalized Hamiltonian representation, we introduce a more general kind of single-parameter fractional infinitesimal transformation of Lie group, the definition and determining equation of fractional conformal invariance are given. And then, we reveal the fractional conformal invariance of Mei symmetry, and the necessary and sufficient condition whether the fractional conformal invariance would be the fractional Mei symmetry is found. In particular, we present the basic theory of fractional conformal invariance of Mei symmetry and it is found that, using the new approach, we can find a new kind of conserved quantity; as a special case, we find that an autonomous fractional generalized Hamiltonian system possesses more conserved quantities. Also, as the new method’s applications, we, respectively, find the conserved quantities of a fractional general relativistic Buchduhl model and a fractional Duffing oscillator led by fractional conformal invariance of Mei symmetry. 相似文献
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This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration. 相似文献
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