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In this paper are study the symmetry of Lagrangians and the conserved quantities for a nonholonomic variable mass system. Firstly, the criterion of the symmetry of Lagrangians for a nonholonomic variable mass system is given. Secondly, the conditions under which there exist a conserved quantity and the form of the conserved quantity, are obtained. Finally, an example is given to illustrate the application of the results.
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Keywords:
- variable mass /
- nonholonomic system /
- symmetry of Lagrangians /
- conserved quantity
[1] Guo Y X, Shang M, Luo S K 2003 Applied Mathematics & Mechanics 24 62 (in Chinese) [郭永新, 尚玫, 罗绍凯 2003 应用数学和力学 24 62]
[2] Mei F X, Xu X J, Zhang Y F 2004 Acta Mech. Sin. 20 668
[3] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量 (北京: 北京理工大学出版社)]
[4] Fang J H, Chen P S, Zhang J 2005 Applied Mathematics & Mechanics 26 187 (in Chinese) [方建会, 陈培胜, 张军 2005 应用数学和力学 26 187]
[5] Jia L Q, Zhang Y Y, Zheng S W 2007 J. Yunnan Univ. 29 589 (in Chinese) [贾利群, 张耀宇, 郑世旺 2007 云南大学学报 (自然科学版) 29 589 ]
[6] Cai J L 2008 Chin. Phys. Lett. 25 1523
[7] Fu J L, Wang X J, Xie F P 2008 Chin. Phys. Lett. 25 2413
[8] Currie D G, Saletan E J 1966 J. Math. Phys. 7 967
[9] Hojman S, Harleston H 1981 J. Math. Phys. 22 1414
[10] Zhao Y Y, Mei F X 1999 Symmetries and invaiants of mechanical systems (Beijing: Science Press) (in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量 (北京:科学出版社)]
[11] Mei F X, Wu H B 2008 Phys. Lett. A 372 2174
[12] Mei F X, Wu H B 2009 Acta Phys. Sin. 58 5916 (in Chinese) [梅凤翔, 吴惠彬 2009 物理学报 58 5919]
[13] Wu H B, Mei F X 2009 Chin. Phys. B 18 3145
[14] Zhang Y, GeWK 2009 Acta Phys. Sin. 58 7447 (in Chinese) [张毅, 葛伟宽 2009 物理学报 58 7447]
[15] Wu H B, Mei F X 2010 Chin. Phys. B 19 030303
[16] Xia L L, Cai J L 2010 Chin. Phys. Lett. 27 080201
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[1] Guo Y X, Shang M, Luo S K 2003 Applied Mathematics & Mechanics 24 62 (in Chinese) [郭永新, 尚玫, 罗绍凯 2003 应用数学和力学 24 62]
[2] Mei F X, Xu X J, Zhang Y F 2004 Acta Mech. Sin. 20 668
[3] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量 (北京: 北京理工大学出版社)]
[4] Fang J H, Chen P S, Zhang J 2005 Applied Mathematics & Mechanics 26 187 (in Chinese) [方建会, 陈培胜, 张军 2005 应用数学和力学 26 187]
[5] Jia L Q, Zhang Y Y, Zheng S W 2007 J. Yunnan Univ. 29 589 (in Chinese) [贾利群, 张耀宇, 郑世旺 2007 云南大学学报 (自然科学版) 29 589 ]
[6] Cai J L 2008 Chin. Phys. Lett. 25 1523
[7] Fu J L, Wang X J, Xie F P 2008 Chin. Phys. Lett. 25 2413
[8] Currie D G, Saletan E J 1966 J. Math. Phys. 7 967
[9] Hojman S, Harleston H 1981 J. Math. Phys. 22 1414
[10] Zhao Y Y, Mei F X 1999 Symmetries and invaiants of mechanical systems (Beijing: Science Press) (in Chinese) [赵跃宇, 梅凤翔 1999 力学系统的对称性与不变量 (北京:科学出版社)]
[11] Mei F X, Wu H B 2008 Phys. Lett. A 372 2174
[12] Mei F X, Wu H B 2009 Acta Phys. Sin. 58 5916 (in Chinese) [梅凤翔, 吴惠彬 2009 物理学报 58 5919]
[13] Wu H B, Mei F X 2009 Chin. Phys. B 18 3145
[14] Zhang Y, GeWK 2009 Acta Phys. Sin. 58 7447 (in Chinese) [张毅, 葛伟宽 2009 物理学报 58 7447]
[15] Wu H B, Mei F X 2010 Chin. Phys. B 19 030303
[16] Xia L L, Cai J L 2010 Chin. Phys. Lett. 27 080201
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