共查询到17条相似文献,搜索用时 93 毫秒
1.
利用代数方程和微分方程在无限小变换下的不变性,研究带有伺服约束的非完整系统的Lie 对称性.给出Lie对称性的确定方程、限制方程、结构方程,并给出守恒量的形式.
关键词:
非完整系统
伺服约束
Lie对称性
守恒量 相似文献
2.
3.
4.
研究非保守力和非完整约束对Hamilton系统的Lie对称性和守恒量的影响.分别研究了Hamilt on系统受到非保守力和非完整约束作用时,系统的Lie对称性保持不变的条件,同时给出了 系统的结构方程和守恒量保持不变的条件.以著名的Emden方程和Appell-Hamel模型为例进行 了分析讨论.
关键词:
分析力学
Hamilton系统
非保守力
非完整约束
对称性
守恒量 相似文献
5.
6.
研究一类非完整系统运动方程的Lie对称性与Hojman型守恒量.给出系统Lie对称性的确定方程和限制方程,存在守恒量的条件以及守恒量的形式.举例说明结果的应用.
关键词:
分析力学
非完整系统
对称性
Hojman型守恒量 相似文献
7.
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
8.
研究奇异系统Hamilton正则方程的形式不变性即Mei对称性,给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系,寻求系统的守恒量.给出一个例子说明结果的应用.
关键词:
奇异系统
Hamilton正则方程
约束
对称性
守恒量 相似文献
9.
研究单面非Chetaev型非完整约束力学系统的对称性与非Noether守恒量.建立了系统的运动微分方程;给出了系统的Lie对称性和Mei对称性的定义和判据;对于单面非Chetaev型非完整系统,证明了在一定条件下,由系统的Lie对称性可直接导致一类新守恒量——Hojman守恒量,由系统的Mei对称性可直接导致一类新守恒量——Mei守恒量;研究了对称性和新守恒量之间的相互关系.文末,举例说明结果的应用.
关键词:
分析力学
单面约束
非完整系统
对称性
Hojman守恒量
Mei守恒量 相似文献
10.
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
11.
The differential equations of motion of a relativistic variable mass system are given.By using the invariance of the differential equations under the infinitesimal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built,and the structure equation and the conserved quantity of the Lie symmetries are obtained.Then the inverse problem of the Lie symmetries is studied.The corresponding Lie symmetries are found according to a known conserved quantity.An example is given to illustrate the application of the result. 相似文献
12.
For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and q_s, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, q_s and \dot{q}_s. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results. 相似文献
13.
A non-Noether conserved quantity, i.e., Hojman conserved quantity, constructed by using Mei symmetry for the nonholonomic controllable mechanical
system, is presented. Under general infinitesimal transformations, the
determining equations of the special Mei symmetry, the constrained restriction equations, the additional restriction equations, and the definitions of the weak Mei symmetry and the strong Mei symmetry of the nonholonomic controllable
mechanical system are given. The condition under which Mei symmetry is a Lie symmetry is obtained. The form of the Hojman conserved quantity of the
corresponding holonomic mechanical system, the weak Hojman conserved
quantity and the strong Hojman conserved quantity of the nonholonomic controllable mechanical system are obtained. An example is given to illustrate the application of the results. 相似文献
14.
研究非完整力学系统的形式不变性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下,给出非完整系统形式不变性的确定方程、约束限制方程和附加限制方程,提出并定义弱(强)形式不变性的概念. 研究特殊形式不变性导致特殊Lie对称性的条件,由系统的特殊形式不变性,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. 给出两个经典例子说明结果的应用.
关键词:
分析力学
非完整系统
形式不变性
非Noether守恒量
Hojman守恒量 相似文献
15.
Jian-Le Cai 《International Journal of Theoretical Physics》2010,49(1):201-211
In this paper the definition of conformal invariance and determining equation for the holonomic system which correspond to
a nonholonomic system of Chetaev’s type are provided. Conformal factor expression is deduced through relationship between
a system’s conformal invariance and Lie symmetry. The necessary and sufficient condition that the system’s conformal invariance
would be Lie symmetry under transformations by the infinitesimal one-parameter transformation group is obtained. The conformal
invariance of weak and strong Lie symmetry for the nonholonomic system of Chetaev’s type is given using restriction equations
and additional restriction equations. And the system’s corresponding conserved quantity is derived with the aid of a structure
equation that gauge function satisfied. Lastly, an example is taken to illustrate the application of the result. 相似文献
16.
In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincarè-Chetaev
equations under the general infinitesimal transformations
of Lie groups is discussed. First, we establish the determining
equations of Lie symmetry of the equations. Second, the Lie symmetrical
non-Noether conserved quantity of the equations is deduced. 相似文献
17.
In the present paper the Lie symmetrical non-Noether conserved
quantity of the Poincaré-Chetaev equations of a generalized
classical mechanics under the general infinitesimal transformations
of Lie groups is discussed. First, we establish the determining
equations of Lie symmetry of the equations. Second, the Lie symmetrical
non-Noether conserved quantity of the equations is deduced. Finally,
an example is given to illustrate the application of the results. 相似文献