| Form Invariance, Noether and Lie Symmetry of Non-conservative Hamiltonian Systems in Phase Space |
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| 作者姓名： | 傅景礼 陈立群 谢凤萍 |
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| 作者单位： | School of Natural Science，Zhejiang University of Science，Zhejiang 310018，P.R. China，Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai 200072，P.R. China，Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai 200072，P.R. China，School of Natural Science，Zhejiang University of Science，Zhejiang 310018，P.R. China |
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| 基金项目： | ProjectsupportedbytheNationalNaturalScienceFoundationofChina (GrantNo .10 3 72 0 5 3 )andtheNationalScienceFounda tionofHenanProvinceGovernment (GrantNo . 0 3 110 114 0 0 ) |
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| 摘 要： | 1 Introduction Thesymmetriesofmechanicalandphysicalsystemshavecloseconnectionwiththeassociatedconservedquantities.Therearetwomethodsforseekingtheconservedquantitiesofthemechanicaland physicalsystems:theNoethersymmetry ,aninvarianceoftheHamiltonactionundertheinfinitesimaltransformationofgroups ,leadingtomanyimportantresults1 5] ;theLiesymmetry ,aninvarianceofthedifferentialequationsundertheinfinitesimaltransformationsofgroups ,extensivelystudiedintherecentyears6 10 ] . Since 2 0 0 0 ,Me…
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Form Invariance, Noether and Lie Symmetry of Non-conservative Hamiltonian Systems in Phase Space |
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| FU Jing-li.Form Invariance, Noether and Lie Symmetry of Non-conservative Hamiltonian Systems in Phase Space[J].Journal of Shanghai University(English Edition),2004(3). |
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| Authors: | FU Jing-li |
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| Institution: | FU Jing-li~ |
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| Abstract: | For the non-conservative holonomic Hamiltonian systems in phase space, the definition and criteria of the form invariance of the generalized Hamilton canonical equations were given. The relations among the form invariance, Noether symmetry and Lie symmetry were studied. The theory of the form invariance for the conservative holonomical systems was worked out. An example was given to illustrate the results. |
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| Keywords: | form invariance Noether symmetry Lie symmetry Hamiltonian system phase space |
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