共查询到20条相似文献,搜索用时 562 毫秒
1.
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
2.
The perturbation to Lie symmetry and adiabatic invariants are studied. Based on the concept of higher-order adiabatic
invariants of mechanical systems with action of a small perturbation, the
perturbation to Lie symmetry is studied, and Hojman adiabatic invariants of Hamilton system are obtained. 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.
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
5.
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
6.
Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems 下载免费PDF全文
For a nonholonomic mechanics system with the action of small disturbance, the Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type are studied under general infinitesimal transformations of groups in which the generalized coordinates and time are variable. On the basis of the invariance of disturbed nonholonomic dynamical equations under general infinitesimal transformations, the determining equations, the constrained restriction equations and the additional restriction equations of Lie symmetries of the system are constructed, which only depend on the variables t, qs and q^.s. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for a nonholonomic system with the action of small disturbance is investigated, and the Lie symmetrical adiabatic invariants, the weakly Lie symmetrical adiabatic invariants and the strongly Lie symmetrical adiabatic invariants of generalized Hojman type of disturbed nonholonomic systems are obtained. An example is given to illustrate applications of the results. 相似文献
7.
8.
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
9.
WANG Peng FANG Jian-Hui DING Ning ZHANG Xiao-Ni 《理论物理通讯》2007,48(4):615-618
In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results. 相似文献
10.
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
11.
12.
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems 总被引:1,自引:0,他引:1
ZHANG Ming-Jiang FANG Jian-Hui LU Kai PANG Ting LIN Peng 《理论物理通讯》2009,51(6):961-966
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained. 相似文献
13.
Based on the concept of adiabatic invariant, the perturbation to Lie-Mei symmetry and adiabatic invariants for Birkhoffian systems are studied. The definition of the perturbation to Lie-Mei symmetry for the system is presented, and the criterion of the perturbation to Lie-Mei symmetry is given. Meanwhile, the Hojman adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained. 相似文献
14.
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
15.
DING Ning FANG Jian-Hui WANG Peng ZHANG Xiao-Ni 《理论物理通讯》2008,49(1):57-60
Based on the concept of adiabatic invariant, perturbation to Lie symmetry and Lutzky adiabatic invariants for Lagrange systems are studied by using different methods from those of previous works. Exact invariants induced from Lie symmetry of the system without perturbation are given. Perturbation to Lie symmetry is discussed and Lutzky adiabatic invariants of the system subject to perturbation are obtained. 相似文献
16.
Based on the concept of adiabatic invariant, the perturbation to
Noether-Lie symmetry and adiabatic invariants for mechanical
systems in phase space are studied. The criterion of the Noether-Lie
symmetry for the perturbed system is given, and the definition of
the perturbation to Noether-Lie symmetry for the system under
the action of small disturbance is presented. Meanwhile, the
Noether adiabatic invariants and the generalized Hojman adiabatic
invariants of the perturbed system are obtained. 相似文献
17.
Based on the concept of adiabatic invariant, the perturbation to the Lie symmetry and adiabatic invariants for general holonomic mechanical systems are studied. The exact invariants induced directly from the Lie symmetry of the system without perturbation are given. The perturbation to the Lie symmetry is discussed and the adiabatic invariants that have the different form from that in [Act. Phys. Sin. 55 (2006) 3236 (in Chinese)] of the perturbed system, are obtained. 相似文献
18.
Based on the concept of adiabatic invariant, the perturbation to the Lie symmetry and adiabatic invariants for general holonomic mechanical systems are studied. The exact invariants induced directly from the Lie symmetry of the system without perturbation are given. The perturbation to the Lie symmetry is discussed and the adiabatic
invariants that have the different form from that in [Act. Phys. Sin. 55 (2006) 3236 (in Chinese)] of the
perturbed system, are obtained. 相似文献
19.
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
20.
研究了Lagrange系统的Lie对称性摄动与新型的非Noether绝热不变量. 列出了未受扰Lagrange系统的Lie对称性导致的Lutzky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Lagrange系统Lie对称性的摄动,得到了系统的一类Lutzky形式的绝热不变量.举例说明方法和结果的应用. 相似文献