共查询到20条相似文献,搜索用时 171 毫秒
1.
2.
3.
把非中心力场中经典粒子运动微分方程写成Ermakov方程的形式,得到Ermakov不变量.用改变时间坐标标度的方法得到用能量H和Ermakov不变量表示的轨道参数方程,并研究两守恒量(能量和Ermakov不变量)相应的无限小变换的Noether对称性、Lie对称性和形式不变性.研究结果表明:与两守恒量相应的无限小变换既具有Noether对称性,也具有Lie对称性和形式不变性.
关键词:
非中心力场
轨道参数方程
守恒量
对称性 相似文献
4.
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
5.
研究非完整力学系统的Noether对称性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下,给出系统的特殊Noether对称性与守恒量,并给出特殊Noether对称性导致特殊Lie对称性的条件. 由系统的特殊Noether对称性,得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出一个例子说明本结果的应用
关键词:
分析力学
非完整系统
Noether对称性
非Noether守恒量
Hojman守恒量 相似文献
6.
7.
8.
9.
10.
11.
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in
the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here
symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic
oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations
leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent.
These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
相似文献
12.
Amin Esfahani 《Physics letters. A》2010,374(35):3635-3645
In this Letter, the existence of the solitary wave solution of the Kadomtsev-Petviashvili equation with generalized evolution and time-dependent coefficients will be studied. We use the solitary wave ansätze-method to derive these solutions. A couple of conserved quantities are also computed. Moreover, some figures are plotted to see the effects of the coefficient functions on the propagation and asymptotic characteristics of the solitary waves. 相似文献
13.
采用变劲度系数的耦合弹簧构建一实际的两自由度弱非线性耦合系统, 用近似Lie对称性理论研究系统的一阶近似Lie对称性与近似守恒量, 得到6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1个一阶近似守恒量为稳定的一阶近似守恒量.
关键词:
两自由度弱非线性耦合系统
近似Lie对称性
近似守恒量 相似文献
14.
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
15.
从一阶近似守恒量的性质出发,把受微扰系统视为未受微扰系统与微扰项的迭加,提出一种分三步求得一阶近似守恒量的新方法:先选择合适的方法求得未受微扰系统的守恒量I0,再考虑微扰项对守恒量I0的影响,最后利用一阶近似守恒量的性质求得一阶近似守恒量.用该方法研究了一实际的受非线性微扰作用的两自由度动力学系统,得到4个稳定的一阶近似守恒量.用坐标变换法和微扰法得到系统一阶近似解的表达式,并讨论4种特殊情况下的一阶近似解. 相似文献
16.
Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system.On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation,the determining equations,the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed.The criterions of Mei symmetries,weak Mei symmetries and strong Mei symmetries of the system are given.New types of conserved quantities,i.e.the Mei symmetrical conserved quantities,the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system,are obtained.Then,a deduction of the first-order nonholonomic system is discussed.Finally,two examples are given to illustrate the application of the method and then the results. 相似文献
17.
We investigate the Hamiltonian H KL with a time-dependent potential in N-dimensional space that is a special combination of a Kepler and a harmonic-oscillator potential. The corresponding classical system has an angular-momentum tensor and a time-dependent analog of the Laplace-Runge-Lenz vector, which commute with the “quasi-Hamiltonian” H c . These quantities are conserved on the orbits of H KL, and their Poisson brackets yield a realization of twisted or untwisted centerless Kac-Moody algebras of so(N+1). The corresponding quantum-mechanical operators and their commutators yield a representation of the positive subalgebras of the above Kac-Moody algebras. 相似文献
18.
19.
The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities 下载免费PDF全文
In this paper, the conserved quantities are constructed using two
methods. The first method is by making an ansatz of the conserved
quantity and then using the definition of Poisson bracket to obtain
the coefficients in the ansatz. The main procedure for the second
method is given as follows. Firstly, the coupled terms in Lagrangian
are eliminated by changing the coordinate scales and rotating the
coordinate axes, secondly, the conserved quantities are obtain in
new coordinate directly, and at last, the conserved quantities are
expressed in the original coordinates by using the inverse transform
of the coordinates. The Noether symmetry and Lie symmetry of the
infinitesimal transformations about the conserved quantities are
also studied in this paper. 相似文献
20.
在增广相空间中研究单面完整约束力学系统的对称性与守恒量.建立了系统的运动微分方程;给出了系统的Norther对称性,Lie对称性和Mei对称性的判据;研究了三种对称性之间的关系;得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量,研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用.
关键词:
分析力学
单面约束
对称性
守恒量
相空间 相似文献