Please wait a minute...
Chin. Phys., 2006, Vol. 15(10): 2197-2201    DOI: 10.1088/1009-1963/15/10/002
GENERAL Prev   Next  

New non-Noether conserved quantities of mechanical system in phase space

Yan Xiang-Hong, Fang Jian-Hui
College of Physics Science and Technology, University of Petroleum,Dongying 257061, China
Abstract  This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new non-Noether conserved quantity of Lie symmetry of the system, and Hojman and Mei's results are of special cases of our conclusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further, obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.
Keywords:  form invariance      phase space      non-Noether conserved quantity      Lie symmetry  
Received:  15 April 2006      Revised:  26 April 2006      Published:  20 October 2006
PACS:  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  45.20.da (Forces and torques)  

Cite this article: 

Yan Xiang-Hong, Fang Jian-Hui New non-Noether conserved quantities of mechanical system in phase space 2006 Chin. Phys. 15 2197

[1] Margolus-Levitin speed limit across quantum to classical regimes based on trace distance
Shao-Xiong Wu(武少雄), Chang-Shui Yu(于长水). Chin. Phys. B, 2020, 29(5): 050302.
[2] Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure
Xin-Yun Hu(胡馨匀), Ke-Jian He(何柯健), Zhong-Hua Li(李中华), Guo-Ping Li(李国平). Chin. Phys. B, 2020, 29(5): 050401.
[3] Study of highly excited vibrational dynamics of HCP integrable system with dynamic potential methods
Aixing Wang(王爱星), Lifeng Sun(孙立风), Chao Fang(房超), Yibao Liu(刘义保). Chin. Phys. B, 2020, 29(1): 013101.
[4] Dynamics of cubic-quintic nonlinear Schrödinger equation with different parameters
Wei Hua(花巍), Xue-Shen Liu(刘学深), Shi-Xing Liu(刘世兴). Chin. Phys. B, 2016, 25(5): 050202.
[5] 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.
[6] Lie symmetry theorem of fractional nonholonomic systems
Sun Yi, Chen Ben-Yong, Fu Jing-Li. Chin. Phys. B, 2014, 23(11): 110201.
[7] Gradient method for blind chaotic signal separation based on proliferation exponent
Lü Shan-Xiang, Wang Zhao-Shan, Hu Zhi-Hui, Feng Jiu-Chao. Chin. Phys. B, 2014, 23(1): 010506.
[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] Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system
Jia Li-Qun, Zhang Mei-Ling, Wang Xiao-Xiao, Han Yue-Lin. Chin. Phys. B, 2012, 21(7): 070204.
[11] 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.
[12] 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.
[13] Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet
Eerdunbuhe,Temuerchaolu. Chin. Phys. B, 2012, 21(3): 035201.
[14] The dynamical properties of a Rydberg hydrogen atom between two parallel metal surfaces
Liu Wei, Li Hong-Yun, Yang Shan-Ying, Lin Sheng-Lu. Chin. Phys. B, 2011, 20(3): 033401.
[15] Phase space reconstruction of chaotic dynamical system based on wavelet decomposition
You Rong-Yi, Huang Xiao-Jing. Chin. Phys. B, 2011, 20(2): 020505.
No Suggested Reading articles found!