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研究广义经典力学系统的对称性和一类新型守恒量——Mei守恒量.在高维增广相空间中建立 了系统的运动微分方程;给出了系统的Mei对称性、Noether对称性和Lie对称性的判据;得 到了分别由三种对称性导致Mei守恒量的条件和Mei守恒量的形式.举例说明结果的应用.
关键词:
广义经典力学
Mei对称性
Noether对称性
Lie对称性
守恒量 相似文献
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研究广义Hamilton系统Lie对称性导致的新型守恒量.首先,建立系统的微分方程.其次,研究一类特殊无限小变换下系统的Lie对称性.第三,将Hojman定理推广到广义Hamilton系统.最后,举例说明结果的应用.
关键词:
广义Hamilton系统
Lie对称性
守恒量 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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SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS 总被引:4,自引:0,他引:4
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In this paper, the symmetries and the conserved quantities for systems of generalized classical mechanics are studied. First, the generalized Noether's theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical action with respect to the action of the infinitesimal transformation of r-parameter finite group of transformation; second, the Lie symmetries and conserved quantities of the systems are studied in accordance with the Lie's theory of the invariance of differential equations under the transformation of infinitesimal groups; and finally, the inner connection between the two kinds of symmetries of systems is discussed. 相似文献
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Kishin Mariwalla 《Physics Reports》1975,20(5):287-362
The object of this review is to discuss methods that enable one to trace the origin of symmetries and conservation laws in mechanics to geometrical symmetries of space-time. Starting with the basic Newtonian assumptions on absolute space and time classical mechanics is developed in configuration space and phase space independently together with the related structures such as force-less mechanics. Heuristic considerations on geometric symmetries in configuration space reveal their intimate relation to conservation laws. Using the methods of differential geometry this relationship is put on a formal footing and symmetry groups of all spherically symmetric single term potentials are classified. The method of infinitesimal canonical transformations is presented as an alternative method of deducing dynamical symmetries of an arbitrary system in phase space. These methods also apply to non-relativistic quantum theory. Possible extension to special and general relatively is also discussed. 相似文献
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Radu Miron 《International Journal of Theoretical Physics》1995,34(7):1123-1146
We study higher-order Lagrangian mechanics on thek-velocity manifold. The variational problem gives rise to new concepts, such as main invariants, Zermelo conditions, higher-order energies, and new conservation laws. A theorem of Noether type is proved for higher-order Lagrangians. The invariants to the infinitesimal symmetries are explicitly written. All this construction is a natural extension of classical Lagrangian mechanics. 相似文献
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A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under infinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finally, an example is given to illustrate the application of the results. 相似文献
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A New Conservation Law Derived from Mei Symmetry for the System
of Generalized Classical Mechanics 总被引:1,自引:0,他引:1
A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under irdinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finadly, an example is given to illustrate the application of the results. 相似文献
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FU JingLi CHEN LiQun & CHEN BenYong Institute of Mathematical Physics Zhejiang Sci-Tech University Hangzhou China 《中国科学:物理学 力学 天文学(英文版)》2010,(3)
We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational f... 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(4):489-504
We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We define higher-degree potential symmetries which then lead to nonlocal conservation laws and nonlocal transformations for the equations. We demonstrate our approach and derive second degree potential symmetries for the Burgers' hierarchy and the Calogero–Degasperis–Ibragimov–Shabat hierarchy. 相似文献
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《中国科学:物理学 力学 天文学(英文版)》2010,(9)
We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results. 相似文献