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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
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The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher order adiabatic invariant of mechanical system with the action of a small perturbation, the form of the exact invariants and adiabatic invariants and
the conditions for their existence are proved. Finally, the inverse problem
of the perturbation to symmetries of the system is studied and an example is
also given to illustrate the application of the results. 相似文献
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In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result. 相似文献
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In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result. 相似文献
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In this paper, we study the Lie symmetrical Hojman conserved quantity of a relativistic mechanical system under general infinitesimal transformations of groups in which the time parameter is variable. The determining equation of Lie symmetry of the system is established. The theorem of the Lie symmetrical Hojman conserved quantity of the system is presented. The above results are generalization to
Hojman's conclusions, in which the time parameter is not variable and the system is non-relativistic. An example is given to illustrate the application of the results in the last. 相似文献
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References: 《理论物理通讯》2007,47(2):213-216
The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints.Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations,this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints.The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced.An example is given to illustrate the application of the results. 相似文献
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A form invariance and a conserved quantity of the generalised Birkhoffian system are studied.
Firstly, a definition and a criterion of the form invariance are given. Secondly, through the form invariance,
a new conserved quantity can be deduced. Finally,
an example is given to illustrate the application of the result. 相似文献
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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
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In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results. 相似文献
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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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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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In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in
phase space are presented. The definition and the criterion for
this system are presented. A new conserved quantity and the
Noether conserved quantity deduced from the Noether-form invariance are obtained. 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
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FANG Jian-Hui WANG Peng DING Ning 《理论物理通讯》2008,49(1):53-56
Two new types of conserved quantities directly deduced by Mei symmetry of holonomic mechanical system are studied. The definition and criterion of Mei symmetry for holonomic system are given. A coordination function is introduced, the conditions under which the Mei symmetry can directly lead to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The result indicates that the coordination function can be selected properly according to the demand of the gauge function, thereby the gauge function can be found out more easily. Furthermore, since the choice of the coordination function has multiformity, much T more conserved quantity of Mei symmetry for holonomic mechanical system can be obtained. 相似文献