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In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results. 相似文献
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Lie Symmetries, Perturbation to Symmetries and Adiabatic Invariants of a Generalized Birkhoff System 总被引:2,自引:0,他引:2
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We study the perturbation to symmetries and adiabatic invariants of a generalized Birkhoff system. Based on the invariance of differential equations under infinitesimal transformations, Lie symmetries, laws of conservations, perturbation to the symmetries and adiabatic invariants of the generalized Birkhoff system are presented. First, the concepts of Lie symmetries and higher order adiabatic invariants of the generalized Birkhoff system are proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate the method and results. 相似文献
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Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics 总被引:1,自引:0,他引:1
QIAO Yong-Fen ZHAO Shu-Hong 《理论物理通讯》2006,46(1):43-45
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result. 相似文献
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QIAO Yong-Fen ZHAO Shu-Hong 《理论物理通讯》2006,46(7)
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result. 相似文献
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In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativisticmechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generaized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results. 相似文献
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ZHAO Shu-Hong LIANG Li-Fu QIAO Yong-Fen 《理论物理通讯》2007,48(5):791-794
We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result. 相似文献
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针对广义Birkhoff系统动力学,提出广义Birkhoff系统动力学的一类逆问题,研究由已知积分流形来建立广义Birkhoff方程. 这类逆问题的解通常不是唯一的,需给出必要的补充要求. 最后举例说明结果的应用.
关键词:
广义Birkhoff系统
动力学逆问题
积分流形 相似文献
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研究广义经典力学系统的对称性与守恒定理.利用常微分方程在无限小变换下的不变性,建 立了系统在高维增广相空间中仅依赖于正则变量的Lie对称变换,并直接由系统的Lie对称性得到了系统的一类守恒律.实际上,这是Hojman的守恒定理对广义经典力学系统的推广.举例说明结果的应用.
关键词:
广义经典力学
对称性
守恒定理 相似文献
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Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems 总被引:3,自引:0,他引:3
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We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems.Firstly,we give the definition of integrating factors for the differential equations of motion of a mechanical system.Next,the necessary conditions for the existemce of the conserved quantities are studied in detail.Then,we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system.Finally,an exampled is given to illustrate the application of the result. 相似文献
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We consider the problem of defining completely a class of additive conservation laws for the generalized Liouville equation whose characteristics are given by an arbitrary system of first-order ordinary differential equations. We first show that if the conservation law, a time-invariant functional, is additive on functions having disjoint compact support in phase space, then it is represented by an integral over phase space of a kernel which is a function of the solution to the Liouville equation. Then we use the fact that in classical mechanics phase space is usually a direct product of physical space and velocity space (Newtonian systems). We prove that for such systems the aforementioned representation of the invariant functionals will hold for conservation laws which are additive only in physical space; i.e., additivity in physical space automatically implies additivity in the whole phase space. We extend the results to include non-degenerate Hamiltonian systems, and, more generally, to include both conservative and dissipative dynamical systems. Some applications of the results are discussed. 相似文献
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Integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics 总被引:2,自引:0,他引:2
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In this paper,we present a general approach to the construction of conservation laws for generalized classical dynamical systems.Firstly,we give the definition of integrating factors and ,secondly,we study in detail the necessary conditions for the existence of conserved quantities.Then we establish the conservation theorem and its inverse for the hamilton‘s canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics.Finally,we give an example to illustrate the application of the results. 相似文献
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《中国物理 B》2015,(5)
The system described by the generalized Birkhoff equations is called a generalized Birkhoffian system. In this paper,the condition under which the generalized Birkhoffian system can be a gradient system is given. The stability of equilibrium of the generalized Birkhoffian system is discussed by using the properties of the gradient system. When there is a parameter in the equations, its influences on the stability and the bifurcation problem of the system are considered. 相似文献
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This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system. 相似文献