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《JOURNAL OF HUNAN UNIVERSITY(NATURNAL SCIENCES)》 1996-01
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Perturbation to the Symmetry of Dynamical Systems and Adiabatic Invariants

Zhao Yueyu(Department of Engineering Mechanics, Hunan Univ, 410082, Changsha,P R China)  
The perturbation problem of symmetry for holonomic conservative dynamical system under small excitation is discussed. We present the concept of high-order adiabatic invariant,and give the form of the adiabatic invariants and the conditions for their existence. Then these results are genealized to the nonholonomic and nonconservative mechanical systems. The relationship between adiabatic invariant and symmetrical transformation is established. It is proved that adiabatic invariant H/ω for linear Hainiltonion system of one degree of freedom is corresponding to the symmetrical transformation about time.
【Fund】: 国家自然科学基金 机械工业部教育科研基金
【CateGory Index】: O316
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【References】
Chinese Journal Full-text Database 2 Hits
1 WANG Xueping;ZHANG Yi;College of Mathematics and Physics,Suzhou University of Science and Technology;College of Civil Engineering,Suzhou University of Science and Technology;;Perturbation to Noether Symmetry and Adiabatic Invariants for Dynamical Systems with Nonstandard Lagrangians[J];Journal of Donghua University(English Edition);2018-01
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【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 ZHOU Jingrun;FU Jingli;Science Teaching and Research Section, Shaoxing Vocational & Technical College;Institute of Mathematical Physics, Zhejiang SCI-tech University;;The Integrating Factor and Conservation Quantity for Constrained Hamilton System[J];力学季刊;2018-03
2 ZHOU Xiao-San;ZHANG Yi;College of Mathematics and Physics,Suzhou University of Science and Technology;Jurong of Secondary Schools;College of Civil Engineering,Suzhou University of Science and Technology;;On Lie symmetry and Mei symmetry for dynamical systems with non-standard Lagrangians[J];云南大学学报(自然科学版);2018-01
3 LIN Wei;ZHU Jianqing;College of Mathematics and Physics,Suzhou University of Science and Technology;;Lie symmetry and conserved quantity for non-conservative systems on time scales[J];华中师范大学学报(自然科学版);2017-06
4 FANG Gang;LUAN Xiwu;LUAN Yigong;The Key Laboratory of Gas Hydrate,Ministry of Land and Resources,Qingdao Institute of Marine Geology;Laboratory for Marine Mineral Resources,Qingdao National Laboratory for Marine Science and Technology;School of Science,China University of Petroleum;;Noether's Theory of Elastic Continuous System[J];吉林大学学报(理学版);2017-05
5 ZHOU Xiao-San;ZHANG Yi;College of Mathematics and Physics,Suzhou University of Science and Technology;College of Civil Engineering,Suzhou University of Science and Technology;;Noether theorems for dynamical systems with non-standard Lagrangians based on El-Nabulsi models[J];四川大学学报(自然科学版);2017-03
6 ZHOU Xiaosan;ZHANG Yi;School of Mathematics and Physics,SUST;School of Civil Engineering,SUST;;Lie symmetries and conserved quantities for dynamical systems with non-standard Lagrangians based on El-Nabulsi models[J];苏州科技学院学报(自然科学版);2016-04
7 ZHANGXiao Cai;ZHANG Yi;College of Mathematics and Physics,Suzhou University of Science and Technology;College of Civil Engineering,Suzhou University of Science and Technology;;Lie symmetry of non-conservative Hamilton system based on fractional model[J];四川大学学报(自然科学版);2016-05
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9 ZHANG Xiaocai;ZHANG Yi;College of Mathematics and Physics,Suzhou University of Science and Technology;College of Civil Engineering,Suzhou University of Science and Technology;;Lie symmetry and conserved quantity of fractional Lagrange system based on El-Nabulsi models[J];中山大学学报(自然科学版);2016-03
10 YAN Bin;ZHANG Yi;School of Mathematics and Physics,SUST;School of Civil Engineering,SUST;;Lagrange symmetry and conserved quantity for a weakly nonholonomic system[J];苏州科技学院学报(自然科学版);2016-01
【Co-references】
Chinese Journal Full-text Database 9 Hits
1 SONG Chuan-Jing;ZHANG Yi;College of Science, Nanjing University of Science and Technology;College of Civil Engineering, Suzhou University of Science and Technology;;Perturbation to Mei Symmetry and Adiabatic Invariants for Disturbed El-Nabulsi's Fractional Birkhoff System[J];Communications in Theoretical Physics;2015-08
2 Chen Ju;Zhang Yi;College of Mathematics and Physics, Suzhou University of Science and Technology;College of Civil Engineering, Suzhou University of Science and Technology;;Exact invariants and adiabatic invariants for nonholonomic systems in non-Chetaev's type based on El-Nabulsi dynamical models[J];物理学报;2015-03
3 Zhang Yi ( College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215009, China );Perturbation to Noether symmetries and adiabatic invariants for nonconservative dynamic systems[J];物理学报;2013-16
4 Ding Ning1) Fang Jian-Hui2) 1) (Institute of Theoretical Science, Department of Physics and Electronics Science, Binzhou University, Binzhou 256603, China) 2) (College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China);A new type of Mei adiabatic invariant induced by perturbation to Mei symmetry for nonholonomic mechanical systems[J];物理学报;2009-11
5 ZHANG Yi FAN Cun-Xin Department of Civil Engineering,University of Science and Technology of Suzhou,Suzhou 215011,China;Perturbation of Symmetries and Hojman Adiabatic Invariants for Mechanical Systems with Unilateral Holonomic Constraints[J];Communications in Theoretical Physics;2007-04
6 Zhang Yi(Department of Civil Engineering,University of Science and Technology of Suzhou,Suzhou 215011,China);Perturbation of symmetries and Hojman adiabatic invariants of discrete mechanical systems in the phase space[J];物理学报;2007-04
7 Luo Shao-Kai (Institute of Mathematical Mechanics and Mathematical Physics,Changsha University,Changsha 410003,China);Mei symmetry,Noether symmetry and Lie symmetry of Hamiltonian canonical equations in a singular system[J];物理学报;2004-01
8 Fu Jing-Li 1)2) Chen Li-Qun 2) Xie Feng-Ping 1) 1)(Insititute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China) 2)(Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China);Perturbation to the symmetries of relativistic Birkhoffian systems and the inverse problems[J];物理学报;2003-11
9 Li Yuan Cheng 1) Zhang Yi 2) Liang Jing Hui 3) 1) (Department of Applied Physics,University of Petroleum,Dongying 257061,China) 2) (Department of Urban Construction, University of Science and Technology of Suzhou, S;Lie symmetries and conserved quantities of a type of nonholonomic singular systems[J];物理学报;2002-10
【Secondary Citations】
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