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This paper studies the Noether symmetry and Mei symmetry of a discrete holonomic mechanical system with variable mass. Firstly, by the difference discrete variation approach, the discrete equations of motion of the system are established. Secondly, the definitions of Noether symmetry and Mei symmetry are given, and the conditions under which the Noether conserved quantity can be induced by Noether symmetry and Mei symmetry are obtained. Finally, an example is discussed to illustrate these results.
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Keywords:
- difference discrete variation /
- variable mass /
- Noether symmetry /
- Mei symmetry
[1] Noether A E 1918 Math. Phys. KI Ⅱ 235
[2] [3] Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[4] Mei F X 2000 J. Beijing Inst. Tech. 9 120
[5] [6] Bluman G W, Kumei S 1989 Symmetries and differential equations (New York: Spinger verlag)
[7] [8] Hojman S A A 1992 J. Phys. A: Math. Gen. 25 L291
[9] [10] [11] Mei F X, Liu R, Luo Y 1991 Advanced analytical mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔, 刘瑞, 罗勇1991高等分析力学(北京: 北京理工大学出版社)]
[12] [13] 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)]
[14] Mei F X 1999 Application of Lie group and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)[梅凤翔1999李群李代数对约束力学系统的应用(北京: 科学出版社)]
[15] [16] Qiao Y F, Zhao S H 2006 Acta Phys. Sin. 55 499 (in Chinese)[乔永芬, 赵淑红 2006 55 499]
[17] [18] [19] Guo Y X, Zhao Z, Liu S X, Wang Y, Zhu N, Han X J 2006 Acta Phys. Sin. 55 3838 (in Chinese)[郭永新, 赵喆, 刘世兴, 王勇, 朱娜, 韩晓静 2006 55 3838]
[20] [21] Wu H B, Mei F X 2006 Acta Phys. Sin. 55 3825 (in Chinese)[吴惠彬, 梅凤翔 2006 55 3825]
[22] [23] Jia L Q, Zhang Y Y, Zheng S W 2007 Acta Phys. Sin. 56 649 (in Chinese)[贾利群, 张耀宇, 郑世旺 2007 56 649]
[24] Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese)[葛伟宽 2008 57 6714]
[25] [26] [27] Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese)[张毅 2012 61 214501]
[28] Lou Z M, Mei F X 2012 Acta Phys. Sin. 61 110201 (in Chinese)[楼智美, 梅凤翔 2012 61 110201]
[29] [30] Marsden J E, West M 2001 Acta Numerica 357
[31] [32] [33] Wendlandt J M, Marsden J E 1997 Physica D 106 223
[34] Cadzow J D 1970 Int. J. Control 11 393
[35] [36] Lee T D 1983 Phys. Lett. B 122 217
[37] [38] Lee T D 1987 J. Statis. Phys. 46 843
[39] [40] Chen J B, Guo H Y, Wu K 2003 J. Math. Phys. 44 1688
[41] [42] [43] Chen J B, Guo H Y, Wu K 2006 Appl. Math. Comput. 177 226
[44] [45] Shi S Y 2008 Ph. D. Dissertation (Shanghai: Shanghai University) (in Chinese)[施沈阳2008博士学位论文(上海: 上海大学)]
[46] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. 37 1
[47] [48] [49] Wu K, Guo H Y 2006 Journal of Captical Normal University 27 1 (in Chinese)[吴可, 郭汉英2006首都师范大学学报27 1]
[50] [51] Lu K, Fang J H, Zhang M J, Wang P 2009 Acta Phys. Sin. 58 7421 (in Chinese)[路凯, 方建会, 张明江, 王鹏 2009 58 7421]
[52] [53] Zhang W W, Fang J H, Zhang B 2012 Jouinal of Dynamics Contral 10 117 (in Chinese)[张伟伟, 方建会, 张斌 2012 动力学与控制学报 10 117]
[54] [55] Liu R W, Zhang H B, Chen L Q 2006 Chin. Phys. 15 249
[56] Fu J L, Chen B Y, Chen L Q 2009 Phys. Lett. A 373 409
[57] [58] [59] Zhang H B, Lv H S, Gu S L 2010 Acta Phys. Sin. 59 5213 (in Chinese)[张宏彬, 吕洪升, 顾书龙 2010 59 5213]
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[1] Noether A E 1918 Math. Phys. KI Ⅱ 235
[2] [3] Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[4] Mei F X 2000 J. Beijing Inst. Tech. 9 120
[5] [6] Bluman G W, Kumei S 1989 Symmetries and differential equations (New York: Spinger verlag)
[7] [8] Hojman S A A 1992 J. Phys. A: Math. Gen. 25 L291
[9] [10] [11] Mei F X, Liu R, Luo Y 1991 Advanced analytical mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese)[梅凤翔, 刘瑞, 罗勇1991高等分析力学(北京: 北京理工大学出版社)]
[12] [13] 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)]
[14] Mei F X 1999 Application of Lie group and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)[梅凤翔1999李群李代数对约束力学系统的应用(北京: 科学出版社)]
[15] [16] Qiao Y F, Zhao S H 2006 Acta Phys. Sin. 55 499 (in Chinese)[乔永芬, 赵淑红 2006 55 499]
[17] [18] [19] Guo Y X, Zhao Z, Liu S X, Wang Y, Zhu N, Han X J 2006 Acta Phys. Sin. 55 3838 (in Chinese)[郭永新, 赵喆, 刘世兴, 王勇, 朱娜, 韩晓静 2006 55 3838]
[20] [21] Wu H B, Mei F X 2006 Acta Phys. Sin. 55 3825 (in Chinese)[吴惠彬, 梅凤翔 2006 55 3825]
[22] [23] Jia L Q, Zhang Y Y, Zheng S W 2007 Acta Phys. Sin. 56 649 (in Chinese)[贾利群, 张耀宇, 郑世旺 2007 56 649]
[24] Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese)[葛伟宽 2008 57 6714]
[25] [26] [27] Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese)[张毅 2012 61 214501]
[28] Lou Z M, Mei F X 2012 Acta Phys. Sin. 61 110201 (in Chinese)[楼智美, 梅凤翔 2012 61 110201]
[29] [30] Marsden J E, West M 2001 Acta Numerica 357
[31] [32] [33] Wendlandt J M, Marsden J E 1997 Physica D 106 223
[34] Cadzow J D 1970 Int. J. Control 11 393
[35] [36] Lee T D 1983 Phys. Lett. B 122 217
[37] [38] Lee T D 1987 J. Statis. Phys. 46 843
[39] [40] Chen J B, Guo H Y, Wu K 2003 J. Math. Phys. 44 1688
[41] [42] [43] Chen J B, Guo H Y, Wu K 2006 Appl. Math. Comput. 177 226
[44] [45] Shi S Y 2008 Ph. D. Dissertation (Shanghai: Shanghai University) (in Chinese)[施沈阳2008博士学位论文(上海: 上海大学)]
[46] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. 37 1
[47] [48] [49] Wu K, Guo H Y 2006 Journal of Captical Normal University 27 1 (in Chinese)[吴可, 郭汉英2006首都师范大学学报27 1]
[50] [51] Lu K, Fang J H, Zhang M J, Wang P 2009 Acta Phys. Sin. 58 7421 (in Chinese)[路凯, 方建会, 张明江, 王鹏 2009 58 7421]
[52] [53] Zhang W W, Fang J H, Zhang B 2012 Jouinal of Dynamics Contral 10 117 (in Chinese)[张伟伟, 方建会, 张斌 2012 动力学与控制学报 10 117]
[54] [55] Liu R W, Zhang H B, Chen L Q 2006 Chin. Phys. 15 249
[56] Fu J L, Chen B Y, Chen L Q 2009 Phys. Lett. A 373 409
[57] [58] [59] Zhang H B, Lv H S, Gu S L 2010 Acta Phys. Sin. 59 5213 (in Chinese)[张宏彬, 吕洪升, 顾书龙 2010 59 5213]
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