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1.
LUO Shao-Kai 《理论物理通讯》2002,38(9)
Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D‘Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained. 相似文献
2.
A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system 总被引:5,自引:0,他引:5
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For a rotational relativistic Birkhoffian system a set of the Lie symmetries and conservation laws is given under infinitesimal transformation. On the basis of the invariance of rotational 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 symmetries are given, and a new type of non-noether conserved quantities are directly obtained from Lie symmetries of the system. An example given to illustrate the application of the results. 相似文献
3.
A Set of Lie Symmetrical Conservation Law for Rotational Relativistic
Hamiltonian Systems 总被引:2,自引:0,他引:2
LUOShao-Kai JIALi-Qun 《理论物理通讯》2003,40(3):265-268
For the rotational relativistic Hamiltonian system, a new type of the Lie symmetries and conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing infinitesimal transformations for generalized coordinates qs and generalized momentums ps, the determining equations of Lie symmetrical transformations of the system are constructed, which only depend on the canonical variables.A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results. 相似文献
4.
For the rotational relativistic Hamiltonian system, a new type of the Lie symmetries and conserved quantitiesare given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, andintroducing infinitesimal transformations for generalized coordinates qs and generalized momentums ps, the determiningequations of Lie symmetrical transformations of the system are constructed, which only depend on the canonical variables.A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example isgiven to illustrate the application of the results. 相似文献
5.
给出转动相对论系统的Appell方程,讨论相对论力学的四个新型基本动力学函数 在无限小群变换下研究转动相对论系统Appell方程的形式不变性,给出定义和判据 研究形式不变性与Noether对称性与Lie对称性的关系,寻求转动相对论系统的守恒量
关键词:
转动相对论 Appell方程 形式不变性 对称性与守恒量 相似文献
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给出相对论系统的Birkhoff函数和Birkhoff函数组、Pfaff作用量、PfaffBirkhoff原理、Birkhoff方程;研究相对论动力学系统的Birkhoff表示方法;根据在无限小变换下相对论Pfaff作用量的不变性和相对论Birkhoff方程的不变性,得到相对论Birkhoff系统的Noether对称性理论和Lie对称性理论;研究相对论Birkhoff系统的代数结构和Poisson积分方法.
关键词:
相对论
Birkhoff系统
Noether对称性
Lie对称性
代数结构
Poisson积分 相似文献
8.
A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems 总被引:4,自引:0,他引:4
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For the relativistic Hamiltonian system, a new type of Lie symmetrical non-Noether conserved quantities are given. On the basis of the theory of invariance of differential equations under infinitesimal transformations, and introducing special infinitesimal transformations for q_s and p_s, we construct the determining equations of Lie symmetrical transformations of the system, which only depend on the canonical variables. A set of non-Noether conserved quantities are directly obtained from the Lie symmetries of the system. An example is given to illustrate the application of the results. 相似文献
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10.
Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems 总被引:1,自引:0,他引:1
LUO Shao-Kai GUO Yong-Xin 《理论物理通讯》2007,47(1):25-30
For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results. 相似文献
11.
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
12.
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
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提出并研究含时滞的非保守系统动力学的Noether对称性与守恒量. 首先,建立含时滞的非保守系统的Hamilton原理,得到含时滞的Lagrange方程;其次,基于含时滞的Hamilton作用量在依赖于广义速度的无限小群变换下的不变性,定义系统的Noether对称变换和准对称变换,建立Noether对称性的判据;最后,研究对称性与守恒量之间的关系,建立含时滞的非保守系统的Noether理论. 文末举例说明结果的应用.
关键词:
时滞系统
非保守力学
Noether对称性
守恒量 相似文献
15.
The differential equations of motion of a relativistic variable mass system are given.By using the invariance of the differential equations under the infinitesimal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built,and the structure equation and the conserved quantity of the Lie symmetries are obtained.Then the inverse problem of the Lie symmetries is studied.The corresponding Lie symmetries are found according to a known conserved quantity.An example is given to illustrate the application of the result. 相似文献
16.
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
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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
17.
In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results. 相似文献
18.
Yi-Ping Luo 《International Journal of Theoretical Physics》2009,48(9):2665-2671
In this paper the generalized conformal symmetries and conserved quantities by Lie point transformations of Hamilton systems
are studied. The necessary and sufficient conditions of conformal symmetry by the action of infinitesimal Lie point transformations
which are simultaneous Lie symmetry are given. This kind type determining equations of conformal symmetry of mechanical systems
are studied. The Hojman conserved quantities of the Hamilton systems under infinitesimal special transformations are obtained.
The relations between conformal symmetries and the Lie symmetries are derived for Hamilton systems. Finally, as application
of the conformal symmetries, an illustration example is introduced. 相似文献
19.
Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems 总被引:1,自引:0,他引:1
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This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system.On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation,the determining equations,the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed.The criterions of Mei symmetries,weak Mei symmetries and strong Mei symmetries of the system are given.New types of conserved quantities,i.e.the Mei symmetrical conserved quantities,the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system,are obtained.Then,a deduction of the first-order nonholonomic system is discussed.Finally,two examples are given to illustrate the application of the method and then the results. 相似文献
20.
研究在小干扰力作用下相对论性Birkhoff系统的对称性摄动问题.建立了相对论性Birkhoff系统的基本原理、运动方程和小扰动方程.讨论该系统的Lie对称性变换和守恒量.研究在无限小变换下该系统的对称性摄动,构造了s阶绝热不变量.给出了绝热不变量存在的条件和形式.研究该系统的对称性摄动逆问题,当系统存在s阶绝热不变量时,得到了该系统的无限小变换的对称性摄动.研究相对论性Birkhoff系统和经典Birkhoff系统对称性摄动之间的关系.
关键词:
Lie对称性
摄动
绝热不变量
相对论 相似文献