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Abstract
This paper focuses on Lagrange symmetries and conserved quantities for nonconservative mechanical systems with nonholonomic constraints of non-Chetaev's type. The definition and criterion of Lagrange symmetry of the systems are given. The conditions under which a Lagrange symmetry can lead to a new conserved quantity（first integral)are obtained and the form of the new conserved quantity（first integral)is presented. Two examples are given to illustrate the application of the results.

Keywords:
nonholonomic system of non-Chetaev’s type/

Lagrange symmetry/

conserved quantity
Authors and contacts
Zhang Yi²,

Ge Wei-Kuan¹
References

Cited By

[1]	Xu Chao, Li Yuan-Cheng.Lie-Mei symmetry and conserved quantities of Nielsen equations for a singular nonholonomic system of Chetaev'type. Acta Physica Sinica, 2013, 62(12): 120201.doi:10.7498/aps.62.120201
[2]	Zheng Shi-Wang, Wang Jian-Bo, Chen Xiang-Wei, Li Yan-Min, Xie Jia-Fang.Lie symmetry and their conserved quantities of Tznoff equations for the vairable mass nonholonomic systems. Acta Physica Sinica, 2012, 61(11): 111101.doi:10.7498/aps.61.111101
[3]	Zhang Bin, Fang Jian-Hui, Zhang Ke-Jun.Symmetry and conserved quantity of Lagrangians for nonholonomic variable mass system. Acta Physica Sinica, 2012, 61(2): 021101.doi:10.7498/aps.61.021101
[4]	Liu Yang-Kui.A kind of conserved quantity of Mei symmetry for general holonomic mechanical systems. Acta Physica Sinica, 2010, 59(1): 7-10.doi:10.7498/aps.59.7
[5]	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
[6]	Zheng Shi-Wang, Xie Jia-Fang, Chen Xiang-Wei, Du Xue-Lian.Another kind of conserved quantity induced directly from Mei symmetry of Tzénoff equations for holonomic systems. Acta Physica Sinica, 2010, 59(8): 5209-5212.doi:10.7498/aps.59.5209
[7]	Li Yuan-Cheng, Xia Li-Li, Wang Xiao-Ming, Liu Xiao-Wei.Lie-Mei symmetry and conserved quantities of Appell equation for a holonomic mechanical system. Acta Physica Sinica, 2010, 59(6): 3639-3642.doi:10.7498/aps.59.3639
[8]	Li Yuan-Cheng, Wang Xiao-Ming, Xia Li-Li.Unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system. Acta Physica Sinica, 2010, 59(5): 2935-2938.doi:10.7498/aps.59.2935
[9]	Li Yuan-Cheng, Xia Li-Li, Wang Xiao-Ming.Unified symmetry of mechanico-electrical systems with nonholonomic constraints of non-Chetaev’s type. Acta Physica Sinica, 2009, 58(10): 6732-6736.doi:10.7498/aps.58.6732
[10]	Cai Jian-Le.Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems. Acta Physica Sinica, 2009, 58(1): 22-27.doi:10.7498/aps.58.22
[11]	Jia Li-Qun, Cui Jin-Chao, Zhang Yao-Yu, Luo Shao-Kai.Lie symmetry and conserved quantity of Appell equation for a Chetaev’s type constrained mechanical system. Acta Physica Sinica, 2009, 58(1): 16-21.doi:10.7498/aps.58.16
[12]	Mei Feng-Xiang, Wu Hui-Bin.Lagrange symmetry for a dynamical system of relative motion. Acta Physica Sinica, 2009, 58(9): 5919-5922.doi:10.7498/aps.58.5919
[13]	Ge Wei-Kuan.Mei symmetry and conserved quantity of a holonomic system. Acta Physica Sinica, 2008, 57(11): 6714-6717.doi:10.7498/aps.57.6714
[14]	Zheng Shi-Wang, Jia Li-Qun.Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems. Acta Physica Sinica, 2007, 56(2): 661-665.doi:10.7498/aps.56.661
[15]	Zheng Shi-Wang, Qiao Yong-Fen.Integrating factors and conservation theorems of Lagrange’s equations for generalized nonconservative systems in terms of quasi-coordinates. Acta Physica Sinica, 2006, 55(7): 3241-3245.doi:10.7498/aps.55.3241
[16]	Zhang Yi.Symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in phase space. Acta Physica Sinica, 2005, 54(10): 4488-4495.doi:10.7498/aps.54.4488
[17]	Zheng Shi-Wang, Fu Jing-Li, Li Xian-Hui.Momentum-dependent symmetries and non-Noether conserved quantities for mechanico-electrical systems. Acta Physica Sinica, 2005, 54(12): 5511-5516.doi:10.7498/aps.54.5511
[18]	Zhang Yi, Mei Feng-Xiang.Effects of constraints on Noether symmetries and conserved quantities in a Birkhoffian system. Acta Physica Sinica, 2004, 53(8): 2419-2423.doi:10.7498/aps.53.2419
[19]	Li Yuan-Cheng, Zhang Yi, Liang Jing-Hui.. Acta Physica Sinica, 2002, 51(10): 2186-2190.doi:10.7498/aps.51.2186
[20]	MEI FENG-XIANG.LIE SYMMETRIES AND CONSERVED QUANTITIES OF NONHOLONOMIC SYSTEMS WITH SERVOCONSTR AINTS. Acta Physica Sinica, 2000, 49(7): 1207-1210.doi:10.7498/aps.49.1207

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Vol. 58, Issue 11 - 2009-06-05

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