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Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomicdynamicM systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equationsand restrictive equations and give three definitions of Lie symmetries before the structure equations and conservedquantities of tile Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example ispresented for illustrating the results. 相似文献
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Lie symmetries and conserved quantities of non—holonomic mechanical systems with unilateral Vacco constraints 总被引:5,自引:0,他引:5 下载免费PDF全文
In this paper,we study the Lie symmetries and the conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints.we give the conditions and the form of conserved quantities due to the Lie symmetries of the systems,and present the inverse problem of the above proble,i.e.finding the corresponding Lie symmetry transformation according to a given integral of the system.Finally,we give an example to illustrate the application of the results. 相似文献
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Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems 总被引:2,自引:0,他引:2 下载免费PDF全文
This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the non-Noether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results. 相似文献
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Yi-Ping Luo 《International Journal of Theoretical Physics》2009,48(9):2665-2671
In this paper the generalized conformal symmetries and conserved quantities by Lie point transformations of Hamilton systems
are studied. The necessary and sufficient conditions of conformal symmetry by the action of infinitesimal Lie point transformations
which are simultaneous Lie symmetry are given. This kind type determining equations of conformal symmetry of mechanical systems
are studied. The Hojman conserved quantities of the Hamilton systems under infinitesimal special transformations are obtained.
The relations between conformal symmetries and the Lie symmetries are derived for Hamilton systems. Finally, as application
of the conformal symmetries, an illustration example is introduced. 相似文献
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In this paper a three-dimensional system with five parameters is considered. For some particular values of these parameters, one finds known dynamical systems. The purpose of this work is to study some symmetries of the considered system, such as Lie-point symmetries, conformal symmetries, master symmetries and variational symmetries. In order to present these symmetries we give constants of motion. Using Lie group theory, Hamiltonian and bi-Hamiltonian structures are given. Also, symplectic realizations of Hamiltonian structures are presented. We have generalized some known results and we have established other new results. Our unitary presentation allows the study of these classes of dynamical systems from other points of view, e.g. stability problems, existence of periodic orbits, homoclinic and heteroclinic orbits. 相似文献
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Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices 下载免费PDF全文
The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results. 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(2):284-304
Abstract After giving a brief account of the Jacobi last multiplier for ordinary differential equations and its known relationship with Lie symmetries, we present a novel application which exploits the Jacobi last multiplier to the purpose of finding Lie symmetries of first-order systems. Several illustrative examples are given. 相似文献
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XIA Li-Li LI Yuan-Cheng WANG Xian-Jun 《理论物理通讯》2009,51(6):1073-1077
The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results. 相似文献
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Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices 下载免费PDF全文
This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme. This
approach makes it possible to devise techniques for solving the Lagrange--Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone. 相似文献
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给出了由Birkhoff系统的Lie对称性求守恒量的一种新方法.研究了系统仅依赖于Birkhoff变量a的Lie对称变换,直接由系统的Lie对称性得到了系统的一类守恒量,并举例说明结果的应用
关键词:
分析力学
对称性
守恒量
Birkhoff系统 相似文献
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研究单面完整约束系统的对称性与守恒量.给出单面完整约束系统Lie对称性的定义,得到了由依赖于速度的一般Lie对称性直接导致的Lutzky守恒量,并给出了它的若干特例:有多余坐标的完整约束系统、非保守力学系统、Lagrange系统的Lutzky守恒量.并举例说明结果的应用.
关键词:
分析力学
单面约束
Lie对称性
Lutzky守恒量 相似文献
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In this paper, we derive Lie point, generalized, master and time-dependent symmetries of a dispersionless equation, which is an extension of a classical long wave system. This equation also admits an infinite-dimensional Lie algebraic structure of Virasoro-type, as in the dispersive integrable systems. We discuss the construction of a sequence of negative ranking symmetries through the property of uniformity in rank. More interestingly, we obtain the conserved quantities directly from the casimir of Poisson pencil. 相似文献
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研究在小干扰力作用下相对论性Birkhoff系统的对称性摄动问题.建立了相对论性Birkhoff系统的基本原理、运动方程和小扰动方程.讨论该系统的Lie对称性变换和守恒量.研究在无限小变换下该系统的对称性摄动,构造了s阶绝热不变量.给出了绝热不变量存在的条件和形式.研究该系统的对称性摄动逆问题,当系统存在s阶绝热不变量时,得到了该系统的无限小变换的对称性摄动.研究相对论性Birkhoff系统和经典Birkhoff系统对称性摄动之间的关系.
关键词:
Lie对称性
摄动
绝热不变量
相对论 相似文献
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The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems 下载免费PDF全文
This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results. 相似文献
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We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity. 相似文献
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《Physics letters. A》2006,359(5):458-466
In the Letter we give new symmetries for the isospectral and non-isospectral Ablowitz–Ladik hierarchies by means of the zero curvature representations of evolution equations related to the Ablowitz–Ladik spectral problem. Lie algebras constructed by symmetries are further obtained. We also discuss the relations between the recursion operator and isospectral and non-isospectral flows. Our method can be generalized to other systems to construct symmetries for non-isospectral equations. 相似文献
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Starting from the structure of the higher order Lie symmetries of the Schrödinger equation in the Euclidean plane E2, we establish, in the case of first-and second-order symmetries, the relations between separation of variables and superintegrable systems in quantum mechanics. 相似文献