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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.
Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
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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
3.
Perturbation to Lie symmetry and another type of Hojman adiabatic invariants for Birkhoffian systems
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The perturbation to Lie symmetry and another type of Hojman adiabatic invariants induced from the perturbation to Lie symmetry for Birkhoffian systems are studied. The exact invariants of Lie symmetry for the system without perturbation are given. Based on the concept of adiabatic invariant, the perturbation to Lie symmetry is discussed and another new type of Hojman adiabatic invariants that have the different form from that in [Acta Phys. Sin. 55 3833] for the perturbed system are obtained. 相似文献
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
DING Ning FANG Jian-Hui 《理论物理通讯》2008,49(6):1410-1412
Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and Noether adiabatic invariants for Birkhoffian systems are studied. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the Noether adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained. 相似文献
11.
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
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.
Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems
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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
14.
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
15.
ZHANG Ming-Jiang FANG Jian-Hui LU Kai 《理论物理通讯》2008,50(8):326-330
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
16.
In this paper, we study the Lie symmetrical Hojman conserved quantity of a relativistic mechanical system under general infinitesimal transformations of groups in which the time parameter is variable. The determining equation of Lie symmetry of the system is established. The theorem of the Lie symmetrical Hojman conserved quantity of the system is presented. The above results are generalization to
Hojman's conclusions, in which the time parameter is not variable and the system is non-relativistic. An example is given to illustrate the application of the results in the last. 相似文献
17.
CHEN Xiang-Wei ZHAO Yong-Hong LI Yan-Min 《理论物理通讯》2005,44(5):773-778
Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic system in terms of quasi-coordinates are studied. The perturbation to symmetries for the nonholonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the forms of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied. 相似文献
18.
CHEN Xiang-Wei ZHAO Yong-Hong LI Yan-Min 《理论物理通讯》2005,44(11)
Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic system in terms of quasi-coordinates are studied. The perturbation to symmetries for the nonholonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the forms of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied. 相似文献
19.
DING Ning FANG Jian-Hui WANG Peng 《理论物理通讯》2007,47(4):594-596
Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system without perturbation are given. The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained. 相似文献
20.
XU Zhi-Xin 《理论物理通讯》2005,44(7)
For a relativistic Birkhoffian system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhoffian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. An example is given to illustrate the application of the results. 相似文献