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Abstract
This paper gives a new type of conserved quantities for Birkhoffian systems. First, the equations of motion of the systems are established, and the definitions and criterions of Mei symmetries are given. Next, an existence theorem for the n ew type of conserved quantities of the systems is given, and the generalized Killing equations used to determine the infinitesimal generators are deduced. Finally, the inverse theorem of the conservation law is established.

Keywords:
Birkhoffian system/

Mei symmetry/

conserved quantity/

Killing equation
Authors and contacts
Zhang Yi²,

Fan Cun-Xin²,

Ge Wei-Kuan¹
References

Cited By

[1]	Han Yue-Lin, Sun Xian-Ting, Zhang Yao-Yu, Jia Li-Qun.Conformal invariance and conserved quantity of Mei symmetry for Appell equations in holonomic system. Acta Physica Sinica, 2013, 62(16): 160201.doi:10.7498/aps.62.160201
[2]	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
[3]	Luo Shao-Kai, Jia Li-Qun, Xie Yin-Li.Mei conserved quantity deduced from Mei symmetry of Appell equation in a dynamical system of relative motion. Acta Physica Sinica, 2011, 60(4): 040201.doi:10.7498/aps.60.040201
[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]	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
[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]	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
[8]	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
[9]	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
[10]	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
[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]	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
[13]	Gu Shu-Long, Zhang Hong-Bin.Mei symmetry, Noether symmetry and Lie symmetry of a Vacco system. Acta Physica Sinica, 2005, 54(9): 3983-3986.doi:10.7498/aps.54.3983
[14]	Fang Jian-Hui, Peng Yong, Liao Yong-Pan.On Mei symmetry of Lagrangian system and Hamiltonian system. Acta Physica Sinica, 2005, 54(2): 496-499.doi:10.7498/aps.54.496
[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]	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]	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
[20]	Zhang Yi.. Acta Physica Sinica, 2002, 51(3): 461-464.doi:10.7498/aps.51.461

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Vol. 53, Issue 11 - 2004-06-05

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