Please wait a minute...
Chin. Phys., 2004, Vol. 13(12): 2182-2186    DOI: 10.1088/1009-1963/13/12/036
RAPID COMMUNICATION Prev  

A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

Huang Fei-Jianga, Lu Yi-Binga, Luo Shao-Kaib
a Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; b Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang University of Sciences, Hangzhou 310018, China; Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China
Abstract  For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and q_s, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, q_s and \dot{q}_s. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.
Keywords:  non-Noether conserved quantity      nonholonomic system      Lie symmetry  
Received:  02 March 2004      Revised:  23 August 2004      Published:  17 March 2005
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Hq (Ordinary differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Hunan Province (Grant No 03JJY3005), and the Scientific Research Foundation of the Education Bureau of Hunan Province, China (Gran

Cite this article: 

Huang Fei-Jiang, Lu Yi-Bing, Luo Shao-Kai A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems 2004 Chin. Phys. 13 2182

[1] Quasi-canonicalization for linear homogeneous nonholonomic systems
Yong Wang(王勇), Jin-Chao Cui(崔金超), Ju Chen(陈菊), Yong-Xin Guo(郭永新). Chin. Phys. B, 2020, 29(6): 064501.
[2] Generalized Chaplygin equations for nonholonomic systems on time scales
Shi-Xin Jin(金世欣), Yi Zhang(张毅). Chin. Phys. B, 2018, 27(2): 020502.
[3] Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm
Shixing Liu(刘世兴), Chang Liu(刘畅), Wei Hua(花巍), Yongxin Guo(郭永新). Chin. Phys. B, 2016, 25(11): 114501.
[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] Lie symmetry theorem of fractional nonholonomic systems
Sun Yi, Chen Ben-Yong, Fu Jing-Li. Chin. Phys. B, 2014, 23(11): 110201.
[6] 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.
[7] Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices
Zhao Gang-Ling, Chen Li-Qun, Fu Jing-Li, Hong Fang-Yu. Chin. Phys. B, 2013, 22(3): 030201.
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet
Eerdunbuhe,Temuerchaolu. Chin. Phys. B, 2012, 21(3): 035201.
[13] Lie–Mei symmetry and conserved quantities of the Rosenberg problem
Liu Xiao-Wei, Li Yuan-Cheng. Chin. Phys. B, 2011, 20(7): 070204.
[14] Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems
Jiang Wen-An, Li Zhuang-Jun, Luo Shao-Kai. Chin. Phys. B, 2011, 20(3): 030202.
[15] Lie symmetry and Mei conservation law of continuum system
Shi Shen-Yang, Fu Jing-Li. Chin. Phys. B, 2011, 20(2): 021101.
No Suggested Reading articles found!