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《ACTA MATHEMATIEA SCIENTIA》 1997-02
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A Generalization of the Poincare-Cartan Invarian and Dirac's Conjecture

Li Ziping; Tang Taiming(Beijing University of Technology, Beijing 100022)  
We generalize Poincar6-Cartan integral invariant to a system with a singular higher-order Lagrangian which depends on time t explicitly, this invariant connected with thecanonical equations and canonical transformation for the generalized constrained Hamiltoniansystem is studied. The connection between this invariant and Dirac's conjecture is discussed.An example shows that Dirac's conjecture fails for a system with a singular higher-order LagranJian.
【Fund】: 国家自然科学基金;;北京市自然科学基金
【CateGory Index】: O413.4
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【References】
Chinese Journal Full-text Database 1 Hits
1 LI Rui-jie, LI Zi-ping( 1. Department of Fundamental Sciences, North China Electric Power University, Beijing 102206, China; 2. College of Applied Sciences, Beijing Polytechnic University, Beijing 100022, China );Generalized Canonical Noether Theorem and Poincare-Cartan Integral Invariant[J];Journal of Beijing Polytechnic University;2002-03
【Citations】
Chinese Journal Full-text Database 1 Hits
1 Li Ziping(Dept. Appl. Phys. Beijing Polytechnlc Unjversity);Poincaré-Cartan Invariant for Constrained Hamiltonian System[J];Journal of Xinjiang University(Natural Science Edition);1991-04
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 Mei Fengxiang Wu Huibin Zhang Yongfa (College of Science and Technology, Beijing Institute of Technology, Beijing, 100081);RESEARCH ADVANCE IN DYNAMICS OF CONSTRAINED SYSTEMS[J];Acta Armamentarii;2000-S1
2 Ge Weikuan(Dept of Physics, Huzhou Teachers College, Huzhou, 313000)Mei Fengxiang(Dept of Applied Mechanics,Beijing Institute of Technology);NOETHER SYMMETRY OF DIFFERENTIAL EQUATION MODELS IN WARFARE[J];Acta Armamentarii;2001-02
3 Li Ziping ( Department of Applied Physics );Canonical Symmetries in Functional Integral Expression for Field Theories[J];Journal of Beijing Polytechnic University;1993-04
4 Li Ziping ( Department of Applied Physics, Beijing Polytechnic University, 100022 );Canonical Symmetries and Conserved Quantities in the Quantization of Functional Integral[J];Journal of Beijing Polytechnic University;1997-03
5 Gao Haixiao Li Ziping ( Department of Applied Physics, Beijing Polytechnic University, 100022 );Noether Theorem and Poincare - Cartan Integral Invariant in Quantum Case for a Constrained Hamilton System[J];Journal of Beijing Polytechnic University;1997-04
6 Li Ziping(Department of Applied Physics, Beijing Polotechnic University, 100022);A Generalization of the Noether Theorem and Its Applications[J];JOURNAL OF BEIJING POLYTECHNIC UNIVERSITY;1994-04
7 Li Ziping(Department of Applied Physics, Beijing Polytechnic Univeroity, 100022);The Generating Functional of Green Function in Phase Space and Feynman's Rule[J];JOURNAL OF BEIJING POLYTECHNIC UNIVERSITY;1995-03
8 MEI Feng xiang (Department of Applied Mechanics, Beijing Institute of Technology, Beijing100081);Integral Invariant of Birkhoff System[J];JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY;2000-01
9 MEI Feng xiang (Dept. of Applied Mechanics, Beijing Institute of Technology, Beijing100081, China);On Noether Symmetry, Lie Symmetry and Form Invariance[J];Journal of Beijing Institute of Technology;2001-04
10 WANG Shu yong 1, GE Wei kuan 2, MEI Feng xiang 1 (1 Dept. of Applied Mechanics, Beijing Institute of Technology, Beijing100081, China; 2 Dept. of Physics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China);Form Invariance of Motion Equations of Holonomic Mechanical Systems[J];Journal of Beijing Institute of Technology;2002-01
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1 Luo Shaokai (Shangqiu Teachers College Shangqiu Henan 476000);Lie Symmetries and Conserved Quantities of Relativistic Holonomic Mechanical Systems[A];[C];2000
2 Zhang Yi (Department of Urban construction,The University of Science and Technology of Suzhou Suzhou 215011 China);Perturbation to Symmetries and Adiabatic Invariant of Holonomic Mechanical Systems with Unilateral Constraints[A];[C];2002
3 Li Yuancheng (Department of Applied Physics,University of Petroleum,Dongying Shandong 257061);Lie Symmetrle and Conserved Quantities of Singular Systems of Variable Mass[A];[C];2002
4 Mei Feng-xiang Wu Hui-bin Shang Mei Zhang Yong-fa (Faculty of Science,Beijing Institute of Technology,Beijing 100081);Mechanization and Solution of Differential Equations[A];[C];2006
5 Wu Run-heng~1 Zhang Wei~2 Wu Hui-bin~2 1.Faculty of Science,North China University of Technology,Beijing,100041 2.Faculty of Science,Beijing Institute of Technology,Beijing,100081;Lie Symmetry and Conserved Quantity for Constrained Hamiltonian Systems[A];[C];2006
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 Gao Haixiao Li Ziping ( Department of Applied Physics, Beijing Polytechnic University, 100022 );Noether Theorem and Poincare - Cartan Integral Invariant in Quantum Case for a Constrained Hamilton System[J];Journal of Beijing Polytechnic University;1997-04
2 LI Zi Ping LI Rui Jie(College of Applied Science, Beijing Polytechnic University, Beijing 100022, China);Generalized Ward Identities for Non-local Transformation[J];High Energh Physics and Nuclear Physics;2002-02
3 LI Rui-Jie LI Zi-Ping (College of Applied Science, Beijing Polytechnic University, Beijing 100022, China);Quantal Canonical Symmetries in Spinor QED with Chern-Simons Term[J];High Energh Physics and Nuclear Physics;2002-04
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5 Li Ziping(Department of Applied Physics, Beijing Polytechnic University, Beijing 100022);Canonical Ward Identities in Generalized QCD[J];HIGH INERGY PHYSICS AND NUCLEAR PHYSICS;1995-05
6 Zhao Yueyu(Department of Engineering Mechanics,Hunan University,Changsha 410012,China);CONSERVATVE QUANTITIES AND LIE'S SYMMETRIES OF NONCONSERVATIVE DYNAMICAL SYSTEMS[J];ACTA MECHANICA SINICA;1994-03
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8 LI ZI-PING Department of Applied Physics, Beijing Polytechnic University, Beijing 100022;SYMMETRY IN CANONICAL FORMALISM OF CONSTRAINED SYSTEM[J];Acta Physica Sinica;1992-05
9 LI ZI-PING (Department of Applied Physics, Beijing Polytechnic University, Beijing 100022);QUANTAL CANONICAL SYMMETRY FOR A SYSTEM WITH SINGULAR HIGHER-ORDER LAGRANGIAN IN FIELD THEORIES[J];Acta Physica Sinica;1996-08
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