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Abstract
In this paper, a new symmetry, i.e., Noether-Lie symmetry and its conserved quantities of the non-holonomic mechanical system is studied. The definition and the criterion of the Noether-Lie symmetry for the system are given. A theorem asserting that the Noether-Lie symmetry for the system leads to both the Noether conserved quantity and the general Hojman conserved quantity is presented. An example is given to illustrate the application of the result. The Hojman conserved quantity of the system is a special case of the general Hojman conserved quantity obtained in this paper.

Keywords:
non-holonomic mechanical system/

Noether-Lie symmetry/

Noether conserved quantity/

general Hojman conserved quantity
Authors and contacts
Fang Jian-Hui,

Ding Ning,

Wang Peng

1.
References

Cited By

[1]	Jia Li-Qun, Sun Xian-Ting, Zhang Mei-Ling, Zhang Yao-Yu, Han Yue-Lin.Generalized Hojman conserved quantity deduced from generalized Lie symmetry of Appell equations for a variable mass mechanical system in relative motion. Acta Physica Sinica, 2014, 63(1): 010201.doi:10.7498/aps.63.010201
[2]	Xu Rui-Li, Fang Jian-Hui, Zhang Bin.The Noether conserved quantity of Lie symmetry for discrete difference sequence Hamilton system with variable mass. Acta Physica Sinica, 2013, 62(15): 154501.doi:10.7498/aps.62.154501
[3]	Xu Chao, Li Yuan-Cheng.Noether-Lie symmetry and conserved quantities of Nielsen equations for a singular variable mass nonholonomic system with unilateral constraints. Acta Physica Sinica, 2013, 62(17): 171101.doi:10.7498/aps.62.171101
[4]	Wang Xiao-Xiao, Sun Xian-Ting, Zhang Mei-Ling, Xie Yin-Li, Jia Li-Qun.Noether symmetry and Noether conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type. Acta Physica Sinica, 2012, 61(6): 064501.doi:10.7498/aps.61.064501
[5]	Liu Xiao-Wei, Li Yuan-Cheng.Noether-Lie symmetry and conserved quantities of the Rosenberg problem. Acta Physica Sinica, 2011, 60(7): 070201.doi:10.7498/aps.60.070201
[6]	Gu Shu-Long, Zhang Hong-Bin.Noether symmetry and the Hojman conserved quantity of the Kepler equation. Acta Physica Sinica, 2010, 59(2): 716-718.doi:10.7498/aps.59.716
[7]	Wang Chuan-Dong, Liu Shi-Xing, Mei Feng-Xiang.Generalized Pfaff-Birkhoff-d’Alembert principle and form invariance of generalized Birkhoff’s equations. Acta Physica Sinica, 2010, 59(12): 8322-8325.doi:10.7498/aps.59.8322
[8]	Dong Wen-Shan, Huang Bao-Xin.Lie symmetries and Noether conserved quantities of generalized nonholonomic mechanical systems. Acta Physica Sinica, 2010, 59(1): 1-6.doi:10.7498/aps.59.1
[9]	Liu Chang, Zhao Yong-Hong, Chen Xiang-Wei.Geometric representation of Noether symmetry for dynamical systems. Acta Physica Sinica, 2010, 59(1): 11-14.doi:10.7498/aps.59.11
[10]	Xia Li-Li, Li Yuan-Cheng, Wang Xian-Jun.Non-Noether conserved quantities for nonholonomic controllable mechanical systems with relativistic rotational variable mass. Acta Physica Sinica, 2009, 58(1): 28-33.doi:10.7498/aps.58.28
[11]	Ding Ning, Fang Jian-Hui.A new type of Mei adiabatic invariant induced by perturbation to Mei symmetry for nonholonomic mechanical systems. Acta Physica Sinica, 2009, 58(11): 7440-7446.doi:10.7498/aps.58.7440
[12]	Cui Jian-Xin, Gao Hai-Bo, Hong Wen-Xue.Mei symmetries and the Noether conserved quantities of super-thin elastic rod. Acta Physica Sinica, 2009, 58(11): 7426-7430.doi:10.7498/aps.58.7426
[13]	Shi Shen-Yang, Huang Xiao-Hong, Zhang Xiao-Bo, Jin Li.The Lie symmetry and Noether conserved quantity of discrete difference variational Hamilton system. Acta Physica Sinica, 2009, 58(6): 3625-3631.doi:10.7498/aps.58.3625
[14]	Xia Li-Li, Li Yuan-Cheng.Non-Noether conserved quantity for relativistic nonholonomic controllable mechanical system with variable mass. Acta Physica Sinica, 2008, 57(8): 4652-4656.doi:10.7498/aps.57.4652
[15]	Zhang Peng-Yu, Fang Jian-Hui.Lie symmetry and non-Noether conserved quantities of variable mass Birkhoffian system. Acta Physica Sinica, 2006, 55(8): 3813-3816.doi:10.7498/aps.55.3813
[16]	Ge Wei-Kuan, Zhang Yi.Lie-form invariance of holonomic mechanical systems. Acta Physica Sinica, 2005, 54(11): 4985-4988.doi:10.7498/aps.54.4985
[17]	Luo Shao-Kai, Guo Yong-Xin, Mei Feng-Xiang.Noether symmetry and Hojman conserved quantity for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(5): 1270-1275.doi:10.7498/aps.53.1270
[18]	Qiao Yong-Fen, Zhao Shu-Hong, Li Ren-Jie.Non Noether conserved quantity of the holonomic mechanical systems in terms of quasi-coordinates ——An extension of Hojman theorem. Acta Physica Sinica, 2004, 53(7): 2035-2039.doi:10.7498/aps.53.2035
[19]	Luo Shao-Kai, Mei Feng-Xiang.A non-Noether conserved quantity, i.e. Hojman conserved quantity, for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(3): 6-10.doi:10.7498/aps.53.6
[20]	Xu Zhi-Xin.. Acta Physica Sinica, 2002, 51(11): 2423-2425.doi:10.7498/aps.51.2423

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Vol. 55, Issue 8 - 2006-04-20

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