Please wait a minute...
Chin. Phys., 2004, Vol. 13(10): 1620-1622    DOI: 10.1088/1009-1963/13/10/007
GENERAL Prev   Next  

The Lie symmetrical non-Noether conserved quantity of holonomic Hamiltonian system

Fang Jian-Huia, Liao Yong-Panb, Peng Yongb
a College of Physics Science and Technology, University of Petroleum, Dongying 257061, China; b Department of Physics, Hexi College, Zhangye 734000, China
Abstract  In this paper, we study the Lie symmetrical non-Noether conserved quantity of a holonomic Hamiltonian system under the general infinitesimal transformations of groups. Firstly, we establish the determining equations of Lie symmetry of the system. Secondly, the Lie symmetrical non-Noether conserved quantity of the system is deduced. Finally, an example is given to illustrate the application of the result.
Keywords:  Hamiltonian system      Lie symmetry      non-Noether conserved quantity  
Received:  30 December 2003      Revised:  31 May 2004      Published:  20 June 2005
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Jr (Partial differential equations)  

Cite this article: 

Fang Jian-Hui, Liao Yong-Pan, Peng Yong The Lie symmetrical non-Noether conserved quantity of holonomic Hamiltonian system 2004 Chin. Phys. 13 1620

[1] Quantum-classical correspondence and mechanical analysis ofa classical-quantum chaotic system
Haiyun Bi(毕海云), Guoyuan Qi(齐国元), Jianbing Hu(胡建兵), Qiliang Wu(吴启亮). Chin. Phys. B, 2020, 29(2): 020502.
[2] Establishment of infinite dimensional Hamiltonian system of multilayer quasi-geostrophic flow & study on its linear stability
Si-xun Huang(黄思训), Yu Wang(王宇), Jie Xiang(项杰). Chin. Phys. B, 2017, 26(11): 114701.
[3] Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola-Kanai oscillator driven by a time-dependent force
Salim Medjber, Hacene Bekkar, Salah Menouar, Jeong Ryeol Choi. Chin. Phys. B, 2016, 25(8): 080301.
[4] Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives
Lin-Li Wang (王琳莉) and Jing-Li Fu(傅景礼). Chin. Phys. B, 2016, 25(1): 014501.
[5] Symmetries and variational calculationof discrete Hamiltonian systems
Xia Li-Li, Chen Li-Qun, Fu Jing-Li, Wu Jing-He. Chin. Phys. B, 2014, 23(7): 070201.
[6] Lie symmetry theorem of fractional nonholonomic systems
Sun Yi, Chen Ben-Yong, Fu Jing-Li. Chin. Phys. B, 2014, 23(11): 110201.
[7] Block basis property of a class of 2×2 operator matrices and its application to elasticity
Song Kuan, Hou Guo-Lin, Alatancang. Chin. Phys. B, 2013, 22(9): 094601.
[8] Lie symmetries and exact solutions for a short-wave model
Chen Ai-Yong, Zhang Li-Na, Wen Shuang-Quan. Chin. Phys. B, 2013, 22(4): 040510.
[9] Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints
Wang Xiao-Xiao, Han Yue-Lin, Zhang Mei-Ling, Jia Li-Qun. Chin. Phys. B, 2013, 22(2): 020201.
[10] A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems
Cui Jin-Chao, Liu Shi-Xing, Song Duan. Chin. Phys. B, 2013, 22(10): 104501.
[11] Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices
Xia Li-Li, Chen Li-Qun. Chin. Phys. B, 2012, 21(7): 070202.
[12] Fractional charges and fractional spins for composite fermions in quantum electrodynamics
Wang Yong-Long, Lu Wei-Tao, Jiang Hua, Xu Chang-Tan, Pan Hong-Zhe. Chin. Phys. B, 2012, 21(7): 070501.
[13] Adaptive H synchronization of chaotic systems via linear and nonlinear feedback control
Fu Shi-Hui, Lu Qi-Shao, Du Ying. Chin. Phys. B, 2012, 21(6): 060507.
[14] Mei conserved quantity directly induced by Lie symmetry in a nonconservative Hamilton system
Fang Jian-Hui,Zhang Bin,Zhang Wei-Wei,Xu Rui-Li. Chin. Phys. B, 2012, 21(5): 050202.
[15] Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Wang Xing-Zhong,Fu Hao,Fu Jing-Li. Chin. Phys. B, 2012, 21(4): 040201.
No Suggested Reading articles found!