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1.
A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems
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In this paper Mei symmetry is introduced for a nonconservative system. The necessary and
sufficient condition for a Mei symmetry to be also a Lie symmetry is
derived. It is proved that the Mei symmetry leads to a non-Noether
conservative quantity via a Lie symmetry, and deduces a Lutzky conservative
quantity via a Lie point symmetry. 相似文献
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对一类完整系统的方程给出其Mei对称性的定义和判据.如果Mei对称性是Noether对称性,则可找到Noether守恒量.如果Mei对称性是Lie对称性,则可找到Hojman型守恒量.举例说明结果的应用.
关键词:
分析力学
完整系统
Mei对称性
守恒量 相似文献
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研究一类动力学方程的Mei对称性的定义和判据,由Mei对称性通过Noether对称性可找到Noether守恒量.由Mei对称性通过Lie对称性可找到Hojman守恒量.同时,也可找到一类新型守恒量. 相似文献
7.
A. Duda 《Acoustical Physics》2006,52(1):36-42
I reanalyze the problem of the existence of longitudinal normals inside the symmetry planes of piezoelectric crystals belonging
to the symmetry class mm2. The equations determining components of longitudinal normals situated outside the symmetry planes for media of this symmetry
are discussed. It is proven that nonpiezoelectric media of rhombic symmetry could have 4 or 8 distinct acoustic axes. Examples
of nonpiezoelectric elastic media of monoclinic symmetry without acoustic axes are given. The method of determination of the
components of acoustic axes for piezoelectric media of arbitrary symmetry is presented. With the help of this method, I discuss
the problem of acoustic axes for piezoelectric media of the symmetry class mm2.
The text was submitted by the author in English. 相似文献
8.
Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems
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In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results. 相似文献
9.
Mei symmetry and generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints
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This paper studies Mei symmetry which leads to a generalized Hojman
conserved quantity for variable mass systems with unilateral
holonomic constraints. The differential equations of motion for the
systems are established, the definition and criterion of the Mei
symmetry for the systems are given. The necessary and sufficient
condition under which the Mei symmetry is a Lie symmetry for the
systems is obtained and a generalized Hojman conserved quantity
deduced from the Mei symmetry is got. An example is given to
illustrate the application of the results. 相似文献
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研究事件空间中单面非Chetaev型非完整系统Nielsen方程的Mei对称性和Mei守恒量.建立系统的运动微分方程,给出系统Mei对称性、弱Mei对称性、强Mei对称性的定义和判据,得到由Mei对称性直接导致的Mei守恒量的存在条件以及Mei守恒量的表达式.举例说明结果的应用.
关键词:
事件空间
Nielsen方程
单面非Chetaev型非完整系统
Mei守恒量 相似文献
12.
Mei symmetry and Mei conserved quantity of nonholonomic systems with unilateral Chetaev type in Nielsen style
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This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results. 相似文献
13.
Symmetry of Tzénoff equations for
unilateral holonomic system under the infinitesimal transformations of
groups is investigated. Its definitions and discriminant equations of Mei
symmetry and Lie symmetry of Tzénoff equations are given. Sufficient and
necessary condition of Lie symmetry deduced by the Mei symmetry is also
given. Hojman conserved quantity of
Tzénoff equations for the system
above through special Lie symmetry and Lie symmetry in the condition of
special Mei symmetry respectively is obtained. 相似文献
14.
研究Chetaev型约束力学系统Appell方程的Lie对称性和Lie对称性直接导致的守恒量.分析Lagrange函数和A函数的关系;讨论Chetaev型约束力学系统Appell方程的Lie对称性导致的守恒量的一般研究方法;在群的无限小变换下,给出Appell方程Lie对称性的定义和判据;得到Lie对称性的结构方程以及Lie对称性直接导致的守恒量的表达式.举例说明结果的应用.
关键词:
Appell方程
Chetaev 型约束力学系统
Lie对称性
守恒量 相似文献
15.
ZHENG Shi-Wang XIE Jia-Fang LI Yan-Min 《理论物理通讯》2008,49(4):851-854
Mei symmetry of Tzenoff equations for nonholonomic systems of non-Chetaev's type under the infinitesimal transformations of groups is studied. Its definitions and discriminant equations of Mei symmetry are given. Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given. Hojman conserved quantity of Tzenoff equations for the systems through Lie symmetry in the condition of special Mei symmetry is obtained. 相似文献
16.
B. Kolakowski 《Solid State Communications》1978,25(11):941-944
It is shown here that real crystals besides their crystallographic symmetry (230 space groups) display another kind of symmetry called in this paper — the dynamic symmetry (1651 Shubnikov groups). The dynamic symmetry manifests itself during transformation by the crystal structure of quantities whose symmetry has two-color operations.An example is given of application of dynamic symmetry for interpretation of phenomenon of forbidden reflexions in an X-ray pattern of ethylidene-N, N′-diacetamide crystals. 相似文献
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Joe Rosen 《Foundations of Physics》1990,20(3):283-307
Five fundamental manifestations of symmetry in physics—reproducibility as symmetry, predictability as symmetry, symmetry of evolution of isolated physical systems, symmetry of states of physical systems, and gauge symmetry—are investigated for their essential meaning and physical significance. The approach is conceptual, to the complete exclusion of mathematical formalism. 相似文献
19.
《Physica D: Nonlinear Phenomena》1988,32(3):423-436
Bifurcation in symmetric is typically associated with spontaneous symmetry breaking. That is, bifurcation is associated with new solution having less symmetry.In this paper we show that symmetry-increasing bifurcation in the discrete dynamics of symmetric mappings is possible (and is perhaps generic). The reason for these bifurcations may be understood as follows. The existence of one attractor in a system with symmetry gives rise to a family of conjugate attractors all related by symmetry. Typically, in computer experiments, what we see is a sequence of symmetry-breaking bifurcations leading to the existence of conjugate chaotic attractors. As the bifurcation parameter is varied these attractors grow in size and merge leading to a single attractor having greater symmetry.We prove a theorem suggesting why this new attractor should have greater symmetry and present a number of striking examples of the symmetric patterns that can be formed by iterating the simplest mappings on the plane with the symmetry of the regular m-gon. In the last section we discuss period-doubling in the presence of symmetry. 相似文献
20.
Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints
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Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results. 相似文献