| 非自治广义Birkhoff系统的Poisson理论 |
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| 引用本文： | 龙梓轩,张毅.非自治广义Birkhoff系统的Poisson理论[J].扬州大学学报(自然科学版),2012(1):16-19. |
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| 作者姓名： | 龙梓轩 张毅 |
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| 作者单位： | 苏州科技学院数理学院;苏州科技学院土木工程学院 |
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| 基金项目： | 国家自然科学基金资助项目(10972151);江苏省普通高校研究生科研创新计划立项项目(CXLX11-0961);苏州科技学院研究生科研创新计划资助项目(SKCX11S-51) |
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| 摘 要： | 研究了非自治广义Birkhoff方程的代数结构,证明非自治广义Birkhoff方程具有相容代数结构和Lie容许代数结构;建立了非自治广义Birkhoff系统的Poisson理论,包括建立系统的Poisson条件,证明了在一定条件下可由已知第一积分得到新的第一积分;讨论了与非自治广义Birkhoff系统的Poisson方法相关的动力学逆问题.结果具有普遍性,非自治Birkhoff系统的情况是该结果的特殊情况.文末举例说明了结果的应用.
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| 关 键 词： | 非自治广义Birkhoff系统 代数结构 Poisson理论 逆问题 |
Poisson theory of a non-autonomous generalized Birkhoffian system |
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| LONG Zi-xuana,ZHANG Yi.Poisson theory of a non-autonomous generalized Birkhoffian system[J].Journal of Yangzhou University(Natural Science Edition),2012(1):16-19. |
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| Authors: | LONG Zi-xuana ZHANG Yi |
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| Institution: | b*(a.Coll of Math & Phys;b.Coll of Civil Engin,Suzhou Univ of Sci & Tech,Suzhou 215009,China) |
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| Abstract: | The algebraic structure of a non-autonomous generalized Birkhoffian system is studied.The results show that a non-autonomous generalized Birkhoffian system has a consistent algebraic structure and a Lie-admissible algebraic structure.The Poisson theory of a non-autonomous generalized Birkhoffian system is established,which includes the establishment of Poisson conditions,and the proposition that under certain conditions a new first integral can be obtained by a known first integral.An inverse problem of dynamics which corresponds to the generalized Poisson method of the non-autonomous generalized Birkhoffian system is studied.The results of this paper are of universal sense,and the circumstance of a non-autonomous Birkhoff system is its special case.Three examples are given to illustrate the application of the results. |
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| Keywords: | non-autonomous Birkhoffian system algebraic structure Poisson theorem inverse problem |
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