| Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems |
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| 作者姓名： | LUO Shao-Kai GUO Yong-Xin |
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| 作者单位： | [1]Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China [2]Depaxtment of Physics, Liaoning University, Shenyang 110036, China |
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| 基金项目： | The project supported by National Natural Science Foundation of China under Grant Nos. 10372053 and 10472040, the Natural Science Foundation of Hunan Province under Grant No. 03JJY3005, the Scientific Research Foundation of Eduction Department of Hunan Province under Grant No. 02C033 and the 0utstanding Young Talents Training Fund of Liaoning Province under Grant No. 309005 |
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| 摘 要： |
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| 关 键 词： | 相对论系统 对称扰动 绝热不变量 数学物理方法 |
| 修稿时间： | 2006-06-29 |
Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems |
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| LUO Shao-Kai GUO Yong-Xin.Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems[J].Communications in Theoretical Physics,2007,47(1):25-30. |
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| Authors: | LUO Shao-Kai GUO Yong-Xin |
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| Abstract: | 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. |
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| Keywords: | relativity BirkhofIian system Lie symmetrical perturbation exact invariant adiabatic invariant of generalized Hojman type |
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