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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
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Hamilton formalism and Noether symmetry for mechanico—electrical systems with fractional derivatives 下载免费PDF全文
This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives.The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established.The definition and the criteria for the fractional generalized Noether quasisymmetry are presented.Furthermore,the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations.An example is presented to illustrate the application of the results. 相似文献
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DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff's analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Baaed on Kirchhoff's analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transfornaationa with rcspect to the radial coordinnte, the gonarnlizod coordinates, and the Cluasi-momenta of 5he model are introduced. The Noether gymmetries and conserved qugntities of the model are obtained. 相似文献
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This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results. 相似文献
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Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry 下载免费PDF全文
This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry.The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given.The conformal factor in the determining equations is found.The relationship between Birkhoff system’s conformal invariance and second-class Mei symmetry are discussed.The necessary and sufficient conditions of conformal invariance,which are simultaneously of second-class symmetry,are given.And Birkhoff system’s conformal invariance may lead to corresponding Mei conserved quantities,which is deduced directly from the second-class Mei symmetry 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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This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equations and restrictive equations and give three definitions of Lie symmetries before the structure equations and conserved quantities of the Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example is presented for illustrating the results. 相似文献
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