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研究奇异Chetaev型非完整系统Nielsen方程的Lie-Mei对称性, 建立系统Nielsen方程的Lie-Mei对称性方程, 给出系统Nielsen方程强Lie-Mei对称性和弱Lie-Mei对称性的定义, 得到对称性导致的Hojman守恒量和Mei守恒量, 最后给出说明性算例.
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关键词:
- 奇异非完整系统 /
- Nielsen方程 /
- Lie-Mei对称性 /
- 守恒量
Using an invariance of differential equations under the infinitesimal transformations of group, we study the Lie-Mei symmetry of Nielsen equations for a singular nonholonomic system of Chetaev'type. We establish the Lie-Mei symmetry equations. The definitions of weak and strong Lie-Mei symmetry are given, and Hojman conserved quantities and Mei conserved quantities are obtained. An example is given to illustrate the application of the results.[1] Noether A E 1918 Math. Phys. KI II 235
[2] Djukić D S, Vujanović B D 1975 Acta Mech. 23 17
[3] Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[4] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[5] Mei F X 2001 Chin. Phys. 10 177
[6] Mei F X, Chen X W 2001 J. Beijing Inst. Technol. 10 138
[7] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整力学基础(北京: 北京工业学院出版社)]
[8] Ge W K, Zhang Y 2005 Acta Phys. Sin. 54 4985 (in Chinese) [葛伟宽, 张毅 2005 54 4985
[9] Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) [张毅 2002 51 461]
[10] Chen X W, Mei F X 2000 Chin. Phys. 9 721
[11] Fu J L, Chen L Q 2003 Chin. Phys. 12 695
[12] Zhang H B 2002 Chin. Phys. 11 1
[13] Xu X J, Mei F X, Qin M C 2004 Acta Phys. Sin. 53 4021 (in Chinese) [许学军, 梅凤翔, 秦茂昌 2004 53 4021]
[14] Wu H B 2005 Chin. Phys. 14 452
[15] Li Y C, Xia L L, Wang X M 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏丽莉, 王小明2010 59 3639]
[16] Jia L Q, Luo S K, Zhang Y Y 2008 Acta Phys. Sin. 57 2006 (in Chinese) [贾利群, 罗绍凯, 张耀宇2008 57 2006]
[17] Cui J C, Jia L Q, Zhang Y Y 2009 Commun. Theor. Phys. 52 7
[18] Li Y C, Wang X M, Xia L L 2010 Acta Phys. Sin. 59 2935 (in Chinese) [李元成, 王小明, 夏丽莉 2010 59 2935]
[19] Xie Y L, Jia L Q, Yang X F 2011 Acta Phys. Sin. 60 030201 (in Chinese) [解银丽, 贾利群, 杨新芳 2011 60 030201]
[20] Li Z P 1991 J. Phys. A: Math. Gen. 24 4261
[21] Li Z P 1992 Chin. Sci. Bull. 37 2204 (in Chinese) [李子平 1992 科学通报 37 2204]
[22] Li Z P 1992 Sci. Sin: Math. 9A 977 (in Chinese) [李子平1992 中国科学: 数学 9A 977]
[23] Zhong S G 1998 Chin. Ann. Math. 19A 361 (in Chinese) [钟寿国1998 数学年刊 19A 361]
[24] Lu K J, Zhang G S 1997 J. Wuhan Univ. (Natural Science Edition) 43 273 (in Chinese) [路可见, 张桂生1997 武汉大学学报 (自然科学版) 43 273]
[25] Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 53 5]
[26] Mei F X, Zhu H P 2000 J. Beijing Inst. Technol. 9 11
[27] Li Y C, Zhang Y, Liang J H 2002 Acta Phys. Sin. 51 2186 (in Chinese) [李元成, 张毅, 梁景辉 2002 51 2186]
[28] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯, 张永发 2008 约束系统动力学研究进展(北京: 科学出版社)]
[29] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanics 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)]
[30] Ding N, Fang J H 2006 Commun.Theor. Phys. 46 265
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[1] Noether A E 1918 Math. Phys. KI II 235
[2] Djukić D S, Vujanović B D 1975 Acta Mech. 23 17
[3] Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
[4] Mei F X 2000 J. Beijing Inst. Technol. 9 120
[5] Mei F X 2001 Chin. Phys. 10 177
[6] Mei F X, Chen X W 2001 J. Beijing Inst. Technol. 10 138
[7] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整力学基础(北京: 北京工业学院出版社)]
[8] Ge W K, Zhang Y 2005 Acta Phys. Sin. 54 4985 (in Chinese) [葛伟宽, 张毅 2005 54 4985
[9] Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese) [张毅 2002 51 461]
[10] Chen X W, Mei F X 2000 Chin. Phys. 9 721
[11] Fu J L, Chen L Q 2003 Chin. Phys. 12 695
[12] Zhang H B 2002 Chin. Phys. 11 1
[13] Xu X J, Mei F X, Qin M C 2004 Acta Phys. Sin. 53 4021 (in Chinese) [许学军, 梅凤翔, 秦茂昌 2004 53 4021]
[14] Wu H B 2005 Chin. Phys. 14 452
[15] Li Y C, Xia L L, Wang X M 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏丽莉, 王小明2010 59 3639]
[16] Jia L Q, Luo S K, Zhang Y Y 2008 Acta Phys. Sin. 57 2006 (in Chinese) [贾利群, 罗绍凯, 张耀宇2008 57 2006]
[17] Cui J C, Jia L Q, Zhang Y Y 2009 Commun. Theor. Phys. 52 7
[18] Li Y C, Wang X M, Xia L L 2010 Acta Phys. Sin. 59 2935 (in Chinese) [李元成, 王小明, 夏丽莉 2010 59 2935]
[19] Xie Y L, Jia L Q, Yang X F 2011 Acta Phys. Sin. 60 030201 (in Chinese) [解银丽, 贾利群, 杨新芳 2011 60 030201]
[20] Li Z P 1991 J. Phys. A: Math. Gen. 24 4261
[21] Li Z P 1992 Chin. Sci. Bull. 37 2204 (in Chinese) [李子平 1992 科学通报 37 2204]
[22] Li Z P 1992 Sci. Sin: Math. 9A 977 (in Chinese) [李子平1992 中国科学: 数学 9A 977]
[23] Zhong S G 1998 Chin. Ann. Math. 19A 361 (in Chinese) [钟寿国1998 数学年刊 19A 361]
[24] Lu K J, Zhang G S 1997 J. Wuhan Univ. (Natural Science Edition) 43 273 (in Chinese) [路可见, 张桂生1997 武汉大学学报 (自然科学版) 43 273]
[25] Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 53 5]
[26] Mei F X, Zhu H P 2000 J. Beijing Inst. Technol. 9 11
[27] Li Y C, Zhang Y, Liang J H 2002 Acta Phys. Sin. 51 2186 (in Chinese) [李元成, 张毅, 梁景辉 2002 51 2186]
[28] Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese) [罗绍凯, 张永发 2008 约束系统动力学研究进展(北京: 科学出版社)]
[29] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanics 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)]
[30] Ding N, Fang J H 2006 Commun.Theor. Phys. 46 265
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