Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems

Zheng Shi-Wang; Jia Li-Qun

doi:10.7498/aps.56.661

Abstract
The Mei symmetry of Tzénoff equations for nonholonomic systems under the infinitesimal transformation of groups is studied in this paper. The definition and the criterion equations of the symmetry are given. If the symmetry is a Lie symmetry, then the Hojman conserved quantity of the Tzénoff equation can be obtained by the Mei symmetry.

Keywords:
nonholonomic system /

Tzénoff equations /

Mei symmetry /

conserved quantity
Authors and contacts
Zheng Shi-Wang²,

Jia Li-Qun¹

(1)江南大学理学院，无锡 214122; (2)商丘师范学院物理与信息工程系，商丘 476000
References

Cited By

[1]	Sun Xian-Ting, Han Yue-Lin, Wang Xiao-Xiao, Zhang Mei-Ling, Jia Li-Qun. A type of new conserved quantity of Mei symmetry for Appell equations in a holonomic system. Acta Physica Sinica, 2012, 61(20): 200204. doi: 10.7498/aps.61.200204
[2]	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
[3]	Cai Jian-Le, Shi Sheng-Shui. Conformal invariance and conserved quantity of Mei symmetry for the nonholonomic system of Chetaev's type. Acta Physica Sinica, 2012, 61(3): 030201. doi: 10.7498/aps.61.030201
[4]	Liu Xiao-Wei, Li Yuan-Cheng. Another kind of conserved quantity induced by Mei symmetry of mechanico-electrical system. Acta Physica Sinica, 2011, 60(11): 111102. doi: 10.7498/aps.60.111102
[5]	Yang Xin-Fang, Sun Xian-Ting, Wang Xiao-Xiao, Zhang Mei-Ling, Jia Li-Qun. Mei symmetry and Mei conserved quantity of Appell equations for nonholonomic systems of Chetaevs type with variable mass. Acta Physica Sinica, 2011, 60(11): 111101. doi: 10.7498/aps.60.111101
[6]	Jia Li-Qun, Zhang Yao-Yu, Yang Xin-Fang, Cui Jin-Chao, Xie Yin-Li. Type Ⅲ structural equation and Mei conserved quantity of Mei symmetry for a Lagrangian system. Acta Physica Sinica, 2010, 59(5): 2939-2941. doi: 10.7498/aps.59.2939
[7]	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
[8]	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
[9]	Fang Jian-Hui. A kind of conserved quantity of Mei symmetry for Lagrange system. Acta Physica Sinica, 2009, 58(6): 3617-3619. doi: 10.7498/aps.58.3617
[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]	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
[12]	Jia Li-Qun, Luo Shao-Kai, Zhang Yao-Yu. Mei symmetry and Mei conserved quantity of Nielsen equation for a nonholonomic system. Acta Physica Sinica, 2008, 57(4): 2006-2010. doi: 10.7498/aps.57.2006
[13]	Hu Chu-Le. Lie symmetries and Hojman conserved quantities of one kind of differential equations of motion of nonholonomic systems. Acta Physica Sinica, 2007, 56(7): 3675-3677. doi: 10.7498/aps.56.3675
[14]	Jia Li-Qun, Zheng Shi-Wang, Zhang Yao-Yu. Mei symmetry and Mei conserved quantity of nonholonomic systems of non-Chetaev’s type in event space. Acta Physica Sinica, 2007, 56(10): 5575-5579. doi: 10.7498/aps.56.5575
[15]	Fang Jian-Hui, Liao Yong-Pan, Peng Yong. Tow kinds of Mei symmeties and conserved quantities of a mechanical system in phase space. Acta Physica Sinica, 2005, 54(2): 500-503. doi: 10.7498/aps.54.500
[16]	Zhang Yi. Symmetries and Mei conserved quantities for systems of generalized classical mechanics. Acta Physica Sinica, 2005, 54(7): 2980-2984. doi: 10.7498/aps.54.2980
[17]	Li Hong, Fang Jian-Hui. Mei symmetry of variable mass systems with unilateral holonomic constraints. Acta Physica Sinica, 2004, 53(9): 2807-2810. doi: 10.7498/aps.53.2807
[18]	Luo Shao-Kai. Mei symmetry, Noether symmetry and Lie symmetry of Hamiltonian system. Acta Physica Sinica, 2003, 52(12): 2941-2944. doi: 10.7498/aps.52.2941
[19]	Qiao Yong-Fen, Zhang Yao-Liang, Han Guang-Cai. Form invariance of Hamilton's canonical equations of a nonholonomic mechanical s ystem. Acta Physica Sinica, 2003, 52(5): 1051-1056. doi: 10.7498/aps.52.1051
[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. 56, Issue 2 - 2007-01-20

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Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems

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