| Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems |
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| 引用本文： | 罗绍凯. Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems[J]. 中国物理快报, 2007, 24(11): 3017-3020 |
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| 作者姓名： | 罗绍凯 |
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| 作者单位： | [1]Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 [2]Key Laboratory of Advanced Textile Materials and Manufacturing Technology （Ministry of Education）, Zhejiang Sci-Tech University, Hangzhou 310018 |
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| 基金项目： | Supported by the National Natural Science Foundation of China under Grant Nos 10372053 and 10472040. |
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| 摘 要： |
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| 关 键 词： | 隔热 不等式 数学物理 不完整系统 |
| 收稿时间： | 2007-05-11 |
Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems |
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| LUO Shao-Kai. Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Disturbed Nonholonomic Systems[J]. Chinese Physics Letters, 2007, 24(11): 3017-3020 |
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| Authors: | LUO Shao-Kai |
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| Affiliation: | Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Ministry of Education), Zhejiang Sci-Tech University, Hangzhou 310018 |
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| Abstract: | 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. |
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| Keywords: | 20.20.Sv 11.30.-j 45.20.Jj |
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