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Mei symmetry and Mei conserved quantity of Nielsen equations in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type are studied. The differential equations of motion of Nielsen equation for the system, the definition and criterion of Mei symmetry, and the expression of Mei conserved quantity deduced directly from Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.
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Keywords:
- nonholonomic constraint of Chetaev's type /
- dynamics of the relative motion /
- Nielsen equation /
- Mei conserved quantity
[1] Djukic D S, Vujanovic B 1975 Acta Mech. 23 17
[2] Lutzky M D 1979 Phys. A: Math. Gen. 12 973
[3] Vujanović B A 1986 Acta Mech. 65 63
[4] Bahar L Y, Kwatry H G 1987 Int. J. Non-Linear Mech. 22 125
[5] Hojman S A 1992 Phys. A: Math. Gen. 25 291
[6] Noether A E 1918 Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl 235
[7] Mei F X 1993 Jiangxi Science 11 1 (in Chinese) [梅凤翔 1993 江西科学 11 1]
[8] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京:科学出版社)]
[9] 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)]
[10] Fu J L, Nie N M, Huang J F 2009 Chin. Phys. B 18 2634
[11] Mei F X, Wu R H, Zhang Y F 1998 Acta Mech. Sin. 30 468 (in Chinese) [梅凤翔, 吴润衡, 张永发 1998 力学学报 30 468]
[12] Luo S K, Guo Y X 2007 Commun. Theor. Phys. 47 25
[13] Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[14] Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[15] Zhang Y 2007 Acta Phys. Sin. 56 3054 (in Chinese) [张毅 2007 56 3054]
[16] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[17] Jiang W A, Li L, Li Z J, Luo S K 2012 Nonlinear Dyn. 67 1075
[18] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) [贾利群, 崔金超, 张耀宇, 罗绍凯 2009 58 16]
[19] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) [梅凤翔, 尚玫 2000 49 1901]
[20] Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470
[21] Zheng S W, Xie J F, Chen X W, Du X L 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向炜, 杜雪莲 2010 59 5209]
[22] Yang X F, Jia L Q, Cui J C, Luo S K 2010 Chin. Phys. B 19 030305
[23] Jia L Q, Xie J F, Luo S K 2008 Chin. Phys. B 17 1560
[24] Mei F X 2000 Journal of Beijing Institute of Technology 9 120 (in Chinese) [梅凤翔 2000 北京理工大学学报 9 120]
[25] Cai J L 2009 Acta Phys. Pol. A 115 854
[26] Cai J L 2010 Acta Phys. Pol. A 117 445
[27] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63
[28] Mei F X 1980 Mech. Eng. 2 61 (in Chinese) [梅凤翔 1980 力学与实践 2 61]
[29] Mei F X 1984 Acta Mech. Sin. 16 596 (in Chinese) [梅凤翔 1984 力学学报 16 596]
[30] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础 (北京:北京工业学院出版社)]
[31] Jia L Q, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 2141 (in Chinese) [贾利群, 张耀宇, 罗绍凯 2009 58 2141]
[32] Mei F X, Liu G L 1987 Foundations of Analytical Mechanics (Xi'an: Xi'an Jiaotong University Press) p91 (in Chinese) [梅凤翔, 刘桂林 1987 分析力学基础(西安:西安交通大学出版社) 第91页]
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[1] Djukic D S, Vujanovic B 1975 Acta Mech. 23 17
[2] Lutzky M D 1979 Phys. A: Math. Gen. 12 973
[3] Vujanović B A 1986 Acta Mech. 65 63
[4] Bahar L Y, Kwatry H G 1987 Int. J. Non-Linear Mech. 22 125
[5] Hojman S A 1992 Phys. A: Math. Gen. 25 291
[6] Noether A E 1918 Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl 235
[7] Mei F X 1993 Jiangxi Science 11 1 (in Chinese) [梅凤翔 1993 江西科学 11 1]
[8] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese) [梅凤翔 1999 李群和李代数对约束力学系统的应用(北京:科学出版社)]
[9] 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)]
[10] Fu J L, Nie N M, Huang J F 2009 Chin. Phys. B 18 2634
[11] Mei F X, Wu R H, Zhang Y F 1998 Acta Mech. Sin. 30 468 (in Chinese) [梅凤翔, 吴润衡, 张永发 1998 力学学报 30 468]
[12] Luo S K, Guo Y X 2007 Commun. Theor. Phys. 47 25
[13] Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[14] Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[15] Zhang Y 2007 Acta Phys. Sin. 56 3054 (in Chinese) [张毅 2007 56 3054]
[16] Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[17] Jiang W A, Li L, Li Z J, Luo S K 2012 Nonlinear Dyn. 67 1075
[18] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) [贾利群, 崔金超, 张耀宇, 罗绍凯 2009 58 16]
[19] Mei F X, Shang M 2000 Acta Phys. Sin. 49 1901 (in Chinese) [梅凤翔, 尚玫 2000 49 1901]
[20] Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470
[21] Zheng S W, Xie J F, Chen X W, Du X L 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向炜, 杜雪莲 2010 59 5209]
[22] Yang X F, Jia L Q, Cui J C, Luo S K 2010 Chin. Phys. B 19 030305
[23] Jia L Q, Xie J F, Luo S K 2008 Chin. Phys. B 17 1560
[24] Mei F X 2000 Journal of Beijing Institute of Technology 9 120 (in Chinese) [梅凤翔 2000 北京理工大学学报 9 120]
[25] Cai J L 2009 Acta Phys. Pol. A 115 854
[26] Cai J L 2010 Acta Phys. Pol. A 117 445
[27] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63
[28] Mei F X 1980 Mech. Eng. 2 61 (in Chinese) [梅凤翔 1980 力学与实践 2 61]
[29] Mei F X 1984 Acta Mech. Sin. 16 596 (in Chinese) [梅凤翔 1984 力学学报 16 596]
[30] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 1985 非完整系统力学基础 (北京:北京工业学院出版社)]
[31] Jia L Q, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 2141 (in Chinese) [贾利群, 张耀宇, 罗绍凯 2009 58 2141]
[32] Mei F X, Liu G L 1987 Foundations of Analytical Mechanics (Xi'an: Xi'an Jiaotong University Press) p91 (in Chinese) [梅凤翔, 刘桂林 1987 分析力学基础(西安:西安交通大学出版社) 第91页]
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