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Abstract
The effects of mass variation on form invariance and conserved quantity of mechanical systems are studied. The criterion of the form invariance for constant mass and variable mass systems is given.By comparing the two criterion equations, the condition under which the form invariance is kept is obtained. The condition under which two systems possess the same conserved quantity is also given. An e xample is given to illustrate the application of the result.

Keywords:
analytical mechanics/

variable mass system/

form invariance/

conserved quantity
Authors and contacts
Ge Wei-Kuan

1.
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Cited By

[1]	Sun Xian-Ting, Zhang Yao-Yu, Xue Xi-Chang, Jia Li-Qun.Form invariance and Mei conserved quantity for generalized Hamilton systems after adding additional terms. Acta Physica Sinica, 2015, 64(6): 064502.doi:10.7498/aps.64.064502
[2]	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
[3]	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
[4]	Liu Yang-Kui, Fang Jian-Hui.Two types of conserved quantities of Lie-Mei symmetry for a variable mass system in phase space. Acta Physica Sinica, 2008, 57(11): 6699-6703.doi:10.7498/aps.57.6699
[5]	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
[6]	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
[7]	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
[8]	Fang Jian－Hui, Zhang Peng－Yu.The conserved quantity of Hojman for mechanicalsystems with variable mass in phase space. Acta Physica Sinica, 2004, 53(12): 4041-4044.doi:10.7498/aps.53.4041
[9]	Fang Jian－Hui, Liao Yong－Pan, Zhang Jun.Non－Noether conserved quantity of a general form for mechanical systems with variable mass. Acta Physica Sinica, 2004, 53(12): 4037-4040.doi:10.7498/aps.53.4037
[10]	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
[11]	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
[12]	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
[13]	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
[14]	Fang Jian-Hui, Chen Pei-Sheng, Zhang Jun, Li Hong.Form invariance and Lie symmetry of relativistic mechanical system. Acta Physica Sinica, 2003, 52(12): 2945-2948.doi:10.7498/aps.52.2945
[15]	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
[16]	Ge Wei-Kuan, Zhang Yi.Form invariance for a constrained system with second-order reducible differentia l constraints. Acta Physica Sinica, 2003, 52(9): 2105-2108.doi:10.7498/aps.52.2105
[17]	Xu Zhi-Xin.. Acta Physica Sinica, 2002, 51(11): 2423-2425.doi:10.7498/aps.51.2423
[18]	Fang Jian-Hui, Xue Qing-Zhong, Zhao Shou-Qing.. Acta Physica Sinica, 2002, 51(10): 2183-2185.doi:10.7498/aps.51.2183
[19]	Li Ren-Jie, Qiao Yong-Fen, Meng Jun.. Acta Physica Sinica, 2002, 51(1): 1-5.doi:10.7498/aps.51.1
[20]	Ge Wei-Kuan.. Acta Physica Sinica, 2002, 51(5): 939-942.doi:10.7498/aps.51.939

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Vol. 54, Issue 6 - 2005-03-20

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