共查询到20条相似文献,搜索用时 15 毫秒
1.
A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems: Adiabatic Invariants of Generalized Lutzky Type 总被引:5,自引:0,他引:5 下载免费PDF全文
For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries t'or a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results. 相似文献
2.
Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems 总被引:1,自引:0,他引:1
LUO Shao-Kai GUO Yong-Xin 《理论物理通讯》2007,47(1):25-30
For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results. 相似文献
3.
Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems 下载免费PDF全文
Based on the invariance of differential equations under
infinitesimal transformations of group, Lie symmetries, exact
invariants, perturbation to the symmetries and adiabatic invariants
in form of non-Noether for a Lagrange system are presented. Firstly,
the exact invariants of generalized Hojman type led directly by Lie
symmetries for a Lagrange system without perturbations are given.
Then, on the basis of the concepts of Lie symmetries and higher
order adiabatic invariants of a mechanical system, the perturbation
of Lie symmetries for the system with the action of small
disturbance is investigated, the adiabatic invariants of generalized
Hojman type for the system are directly obtained, the conditions for
existence of the adiabatic invariants and their forms are proved.
Finally an example is presented to illustrate these results. 相似文献
4.
5.
Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems 下载免费PDF全文
Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants, i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results. 相似文献
6.
研究相空间中离散力学系统对称性的摄动与绝热不变量.列出相空间中未受扰离散力学系统的特殊Lie对称性导致的Hojman型精确不变量.基于相空间中力学系统的高阶绝热不变量的定义,研究在小扰动作用下系统Lie对称性的摄动,得到了相空间中离散力学系统的一类新的绝热不变量——Hojman型绝热不变量.举例说明结果的应用.
关键词:
相空间
Lie对称性
摄动
绝热不变量 相似文献
7.
Lie Symmetries, Perturbation to Symmetries and Adiabatic Invariants of a Generalized Birkhoff System 总被引:2,自引:0,他引:2 下载免费PDF全文
We study the perturbation to symmetries and adiabatic invariants of a generalized Birkhoff system. Based on the invariance of differential equations under infinitesimal transformations, Lie symmetries, laws of conservations, perturbation to the symmetries and adiabatic invariants of the generalized Birkhoff system are presented. First, the concepts of Lie symmetries and higher order adiabatic invariants of the generalized Birkhoff system are proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate the method and results. 相似文献
8.
ZHANG Xiao-Ni FANG Jian-Hui LIN Peng PANG Ting 《理论物理通讯》2008,49(4):855-858
Based on the concept of higher-order adiabatic invariants of mechanical system with action of a small perturbation, the perturbation to Lie symmetry and generalized Hojman adiabatic invariants for the relativistic Hamilton system are studied. Perturbation to Lie symmetry is discussed under general infinitesimal transformation of groups in which time is variable. The form and the criterion of generalized Hojman adiabatic jnvariants for this system are obtained. Finally, an example is given to illustrate the results. 相似文献
9.
10.
研究Birkhoff系统对称性的摄动与绝热不变量.给出了未受扰Birkhoff系统的Lie对称性导致的Hojman型精确不变量.基于力学系统的高阶绝热不变量的定义,研究在小扰动作用下Birkhoff系统Lie对称性的摄动,得到了系统的一类新型绝热不变量.举例说明结果的应用.
关键词:
Birkhoff系统
Lie对称性
摄动
绝热不变量 相似文献
11.
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
12.
13.
研究事件空间中完整力学系统Lie对称性的摄动与绝热不变量.基于力学系统的高阶绝热不变量的概念,研究在小扰动作用下系统Lie对称性的摄动,得到了事件空间中完整力学系统的一类Hojman形式的高阶绝热不变量,给出了绝热不变量存在的条件及形式.并举例说明结果的应用.
关键词:
事件空间
对称性
摄动
绝热不变量 相似文献
14.
A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics 总被引:1,自引:0,他引:1 下载免费PDF全文
The perturbations to symmetries and adiabatic invariants for nonconservative systems
of generalized classical mechanics are studied. The exact invariant in the form of
Hojman from a particular Lie symmetry for an undisturbed system of generalized
mechanics is given. Based on the concept of high-order adiabatic invariant in
generalized mechanics, the perturbation to Lie symmetry for the system under the
action of small disturbance is investigated, and a new adiabatic invariant for the
nonconservative system of generalized classical mechanics is obtained, which can be
called the Hojman adiabatic invariant. An example is also given to illustrate the
application of the results. 相似文献
15.
Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints 下载免费PDF全文
This paper studies the perturbation to symmetries and adiabatic
invariant for nonholonomic controllable mechanical systems with
non-Chetaev type constraints. It gives the exact invariants
introduced by the Lie symmetries of the nonholonomic controllable
mechanical system with non-Chetaev type constraints without
perturbation. Based on the definition of high-order adiabatic
invariants of mechanical system, the perturbation of Lie symmetries
for nonholonomic controllable mechanical system with non-Chetaev type
constraints with the action of small disturbances is investigated,
and a new type of adiabatic invariant of system are obtained. In the
end of this paper, an example is given to illustrate the application
of the results. 相似文献
16.
Perturbation of Symmetries and Hojman Adiabatic Invariants for Mechanical Systems with Unilateral Holonomic Constraints 总被引:1,自引:0,他引:1
ZHANG Yi FAN Cun-Xin 《理论物理通讯》2007,47(4):607-610
The perturbation of symmetries and adiabatic invariants for mechanical systems with unilateral holonomic constraints are studied. The exact invariant in the form of Hojman led by special Lie symmetries for an undisturbed system with unilateral constraints is given. Based on the concept of high-order adiabatic invariant of mechanical systems, the perturbation of Lie symmetries for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the system with unilateral holonomic constraints is obtained, which can be called Hojman adiabatic invariant. In the end of the paper, an example is given to illustrate the application of the results. 相似文献
17.
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
18.
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
19.
20.
基于El-Nabulsi动力学模型,研究了小扰动作用下Birkhoff系统Noether对称性的摄动与绝热不变量问题.首先,将El-Nabulsi提出的在分数阶微积分框架下基于Riemann-Liouville分数阶积分的非保守系统动力学模型拓展到Birkhoff系统,建立El-Nabulsi-Birkhoff方程;其次,基于在无限小变换下El-Nabulsi-Pfaff作用量的不变性,给出Noether准对称性的定义和判据,得到了Noether对称性导致的精确不变量;再次,引入力学系统的绝热不变量概念,研究El-Nabulsi动力学模型下受小扰动作用的Birkhoff系统Noether对称性的摄动与绝热不变量之间的关系,得到了对称性摄动导致的绝热不变量的条件及其形式.作为特例,给出了El-Nabulsi动力学模型下相空间中非保守系统和经典Birkhoff系统的Noether对称性的摄动与绝热不变量.以著名的Hojman-Urrutia问题为例,研究其在El-Nabulsi动力学模型下的Noether对称性,得到了相应的精确不变量和绝热不变量. 相似文献