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Abstract
A form invariance for mechanical systems with second_order reducible differential constraints is studied．Two methods to study the form invariance of the systems are used．In the first method，the system is considered as a nonholonomic system with second_order and in the second method it is considered as a system after reduction．The relation between the two methods is obtained．The result proves that it is possible that some symmetries are lost in the second method．

Keywords:
constrained mechanical system/

differential constraint/

reduction/

form invarian ce/

conserved quantity
Authors and contacts
Ge Wei-Kuan¹,

Zhang Yi²
References

Cited By

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[2]	Wang Ting-Zhi, Sun Xian-Ting, Han Yue-Lin.Conformal invariance and conserved quantity of relative motion holonomic dynamical system in phase space. Acta Physica Sinica, 2014, 63(10): 104502.doi:10.7498/aps.63.104502
[3]	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
[4]	Chen Xiang-Wei, Zhao Yong-Hong, Liu Chang.Conformal invariance and conserved quantity for holonomic mechanical systems with variable mass. Acta Physica Sinica, 2009, 58(8): 5150-5154.doi:10.7498/aps.58.5150
[5]	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
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[7]	Hu Chu-Le, Xie Jia-Fang.Form invariance and Hojman conserved quantity of Maggi equation. Acta Physica Sinica, 2007, 56(9): 5045-5048.doi:10.7498/aps.56.5045
[8]	Qiao Yong-Fen, Zhao Shu-Hong.Form invariance and non-Noether conserved quantity of generalized Raitzin’s canonical equations of non-conservative system. Acta Physica Sinica, 2006, 55(2): 499-503.doi:10.7498/aps.55.499
[9]	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
[10]	Lou Zhi-Mei.Form invariance for Hamiltonian Ermakov systems. Acta Physica Sinica, 2005, 54(5): 1969-1971.doi:10.7498/aps.54.1969
[11]	Ge Wei-Kuan.Effects of mass variation on form invariance and conserved quantity of mechanical systems. Acta Physica Sinica, 2005, 54(6): 2478-2481.doi:10.7498/aps.54.2478
[12]	Xu Xue-Jun, Mei Feng-Xiang, Qin Mao-Chang.A nonNoether conserved quantity constructed using form invariance for Nielsen equation of a non-conservativemechanical system. Acta Physica Sinica, 2004, 53(12): 4021-4025.doi:10.7498/aps.53.4021
[13]	Luo Shao-Kai, Guo Yong-Xin, Mei Feng-Xiang.Form invariance and Hojman conserved quantity for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(8): 2413-2418.doi:10.7498/aps.53.2413
[14]	Lou Zhi-Mei.Form invariance of second-order linear nonholonomic systems in phase space. Acta Physica Sinica, 2004, 53(7): 2046-2049.doi:10.7498/aps.53.2046
[15]	Zhang Yi.Form invariance of mechanical systems with unilateral holonomic constraints. Acta Physica Sinica, 2004, 53(2): 331-336.doi:10.7498/aps.53.331
[16]	Fang Jian-Hui, Yan Xiang-Hong, Chen Pei-Sheng.Form invariance and Noether symmetry of a relativistic mechanical system. Acta Physica Sinica, 2003, 52(7): 1561-1564.doi:10.7498/aps.52.1561
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[18]	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
[19]	Fang Jian-Hui, Xue Qing-Zhong, Zhao Shou-Qing.. Acta Physica Sinica, 2002, 51(10): 2183-2185.doi:10.7498/aps.51.2183
[20]	Ge Wei-Kuan.. Acta Physica Sinica, 2002, 51(5): 939-942.doi:10.7498/aps.51.939

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Vol. 52, Issue 9 - 2003-05-05

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