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Abstract
It is showed that Stability of Birkhoffian system can be determined by its conserved quantities. If a conserved quantity or a combination of some conserved quantities became a Liapunov function,then it can be used to study the stability of equilibrium and the stability of motion of the system.

Keywords:
Birkhoffian system/

conserved quantity/

Liapunov stability
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Xu Zhi-Xin

1.
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Cited By

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[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]	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
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[5]	Ding Guang-Tao.Hojman method for construction of Birkhoffian representation and the Birkhoff symmetry. Acta Physica Sinica, 2010, 59(6): 3643-3647.doi:10.7498/aps.59.3643
[6]	Zhang Yi.Birkhoff symmetries and conserved quantities of generalized Birkhoffian systems. Acta Physica Sinica, 2009, 58(11): 7436-7439.doi:10.7498/aps.58.7436
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[8]	Cai Jian-Le, Mei Feng-Xiang.Conformal invariance and conserved quantity of Lagrange systems under Lie point transformation. Acta Physica Sinica, 2008, 57(9): 5369-5373.doi:10.7498/aps.57.5369
[9]	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
[10]	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
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Vol. 54, Issue 10 - 2005-05-20

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