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研究广义Hamilton系统在无限小变换下的共形不变性与Mei对称性,给出系统共形不变性同时是Mei对称性的充分必要条件,得到广义Hamilton系统共形不变性导致的Mei守恒量,举例说明结果的应用. 相似文献
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研究一般完整系统Mei对称性的共邢不变性与守恒量.引入无限小单参数变换群及其生成元向量,定义一般完整系统动力学方程的Mei对称性共形不变性,借助Euler算子导出Mei对称性共形不变性的相关条件,给出其确定方程.讨论共形不变性与Noether对称性、Lie对称性以及Mei对称性之间的关系.利用规范函数满足的结构方程得到系统相应的守恒量.举例说明结果的应用.
关键词:
一般完整系统
Mei对称性
共形不变性
守恒量 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 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 conserved quantities of Appell systems under second-class Mei symmetry 总被引:2,自引:0,他引:2 下载免费PDF全文
In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system’s conformal invariance and Mei symmetry are discussed. And Appell system’s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result. 相似文献
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Conformal invariance and Hojman conserved quantities for holonomic systems with quasi-coordinates 下载免费PDF全文
We propose a new concept of the conformal invariance and the conserved quantities for holonomic systems with quasi-coordinates. A one-parameter infinitesimal transformation group and its infinitesimal transformation vector of generators for holonomic systems with quasi-coordinates are described in detail. The conformal factor in the determining equations of the Lie symmetry is found. The necessary and sufficient conditions of conformal invariance, which are simultaneously of Lie symmetry, are given. The conformal invariance may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Finally, an illustration example is introduced to demonstrate the application of the result. 相似文献
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Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems 下载免费PDF全文
This paper studies conformal invariance and generalized
Hojman conserved quantities of mechanico-electrical systems. The
definition and the determining equation of conformal invariance for
mechanico-electrical systems are provided. The conformal factor
expression is deduced from conformal invariance and Lie symmetry
under the infinitesimal single-parameter transformation group. The
generalized Hojman conserved quantities from the conformal
invariance of the system are given. An example is given to
illustrate the application of the result. 相似文献
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The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of the rotational relativistic Pfaff-Birkhoff-D'Alembert principle under infinitesimal transformations, the Noether symmetries and conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotational relativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of the rotational relativistic Birkhoff system are given. 相似文献
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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
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This paper studies a new conserved quantity which can be called
generalized Mei conserved quantity and directly deduced by Mei
symmetry of Birkhoff system. The conditions under which the Mei
symmetry can directly lead to generalized Mei conserved quantity and
the form of generalized Mei conserved quantity are given. An example
is 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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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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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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In this paper the conformal invariance by infinitesimal
transformations of first-order Lagrange systems is discussed in detail. The
necessary and sufficient conditions of conformal invariance by the action of
infinitesimal transformations being Lie symmetry simultaneously are given.
Then we get the conserved quantities of conformal invariance by the
infinitesimal transformations. Finally an example is given to illustrate
the application of the results. 相似文献