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Noether symmetry and Noether conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev's type are studied. The differential equation of motion of Nielsen equation for the system, the definition and the criterion of Noether symmetry, and the expression of Noether conserved quantity deduced directly from Noether 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 /
- Noether conserved quantity
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[2] [3] Li Y,Fang J H,Zhang K J 2010 Journal of Dynamics and Control 8 300 (in Chinese) [李燕,方建会,张克军 2010动力学与控制学报 8 300]
[4] Luo S K,Jia L Q,Cai J L 2005 Commun.Theor.Phys.43 193
[5] [6] Chen X W,Luo S K,Mei F X 2002 Applied Mathematics and Mechanics 23 47 (in Chinese)[陈向炜,罗绍凯,梅凤翔 2002 应用数学和力学 23 47]
[7] [8] Zhou Y X 2010 Journal of Zaozhuang University 27 6 (in Chinese)[周玉霞 2010 枣庄学院学报 27 6]
[9] [10] Zhang Y,Mei F X 2004 Acta Phys.Sin.53 2419 (in Chinese) [张毅,梅凤翔 2004 53 2419]
[11] [12] Fu J L,Nie N M,Huang J F 2009 Chin.Phys.B 18 2634 (in Chinese)
[13] [14] Luo S K 2007 Chin.Phys.Lett.24 2463
[15] [16] [17] Luo S K 2007 Acta Phys.Sin.57 5580 (in Chinese) [罗绍凯 2007 57 5580]
[18] Luo S K,Huang F J,Lu Y B 2004 Chin.Phys.13 2182
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[22] Mei F X,Shang M 2000 Acta Phys.Sin.49 1901 (in Chinese) [梅凤翔,尚玫 2000 58 16]
[23] [24] Luo S K,Chen X W,Guo Y X 2007 Chin.Phys.16 3176
[25] [26] Luo S K 2007 Chin.Phys.Lett.24 2463
[27] [28] [29] Jia L Q,Zhang Y Y,Zheng S W 2007 Journal of Ynunan University 29 589 (in Chinese) [贾利群,张耀宇,郑世旺 2007 云南大学学报 29 589]
[30] 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]
[31] [32] 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]
[33] [34] 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]
[35] [36] [37] Yang X F,Jia L Q,Cui J C,Luo S K 2010 Chin.Phys.B 19 030305
[38] [39] Jia L Q,Xie J F,Luo S K 2008 Chin.Phys.B 17 1560
[40] [41] Cai J L 2009 Acta Phys.Sin.58 22 (in Chinese) [蔡建乐 2009 58 22]
[42] Djukic D S,Vujanovic B 1975 Acta Mechanica 23 17
[43] [44] Bahar L Y,Kwatry H G 1987 Int.J.Non-Linear Mech.22 125
[45] [46] [47] Li Z P 1981 Acta Phys.Sin.20 1659 (in Chinese) [李子平 1981 20 1659]
[48] Li Z P 1991 J.Phys.A:Math.Gen.24 4261
[49] [50] Li Z P 1993 Classical and Quantum Constrained Systems and Symmetry (Beijing:Beijing industrial university Press) (in Chinese)[李子平 1993 经典和量子约束系统及其对称性质(北京:北京工业大学出版社)]
[51] [52] [53] Dong W S,Huang B X,Fang J H 2011 Chin.Phys.B 20 010204
[54] [55] Xia L L,Shan L F 2010 Chin.Phys.B 19 090302
[56] Luo S K 2007 Chin.Phys.16 3182
[57] [58] [59] Shi Y,Fu R,Ma S J 2007 Journal of University of Science and Technology of Suzhou (Natural Science Edition) 24 34 (in Chinese)[施勇,傅蓉,马善钧 2007 苏州科技学院学报 (自然科学版) 24 34]
[60] [61] Ma S J,Liu M P,Huang P T 2005 Chin.Phys.14 244
[62] Mei F X,Shui X P 2006 Journal of Beijing Institute of Technology 26 285 (in Chinese) [梅凤翔,水小平 2006 北京理工大学学报 26 285]
[63] [64] [65] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems(Beijing:Beijing Institute of Industrial 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)]
[66] 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)]
[67] -
[1] Noether A E 1918 Nachr.Akad.Wiss.G ttingen.Math.Phys.KIII 235
[2] [3] Li Y,Fang J H,Zhang K J 2010 Journal of Dynamics and Control 8 300 (in Chinese) [李燕,方建会,张克军 2010动力学与控制学报 8 300]
[4] Luo S K,Jia L Q,Cai J L 2005 Commun.Theor.Phys.43 193
[5] [6] Chen X W,Luo S K,Mei F X 2002 Applied Mathematics and Mechanics 23 47 (in Chinese)[陈向炜,罗绍凯,梅凤翔 2002 应用数学和力学 23 47]
[7] [8] Zhou Y X 2010 Journal of Zaozhuang University 27 6 (in Chinese)[周玉霞 2010 枣庄学院学报 27 6]
[9] [10] Zhang Y,Mei F X 2004 Acta Phys.Sin.53 2419 (in Chinese) [张毅,梅凤翔 2004 53 2419]
[11] [12] Fu J L,Nie N M,Huang J F 2009 Chin.Phys.B 18 2634 (in Chinese)
[13] [14] Luo S K 2007 Chin.Phys.Lett.24 2463
[15] [16] [17] Luo S K 2007 Acta Phys.Sin.57 5580 (in Chinese) [罗绍凯 2007 57 5580]
[18] Luo S K,Huang F J,Lu Y B 2004 Chin.Phys.13 2182
[19] [20] [21] 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]
[22] Mei F X,Shang M 2000 Acta Phys.Sin.49 1901 (in Chinese) [梅凤翔,尚玫 2000 58 16]
[23] [24] Luo S K,Chen X W,Guo Y X 2007 Chin.Phys.16 3176
[25] [26] Luo S K 2007 Chin.Phys.Lett.24 2463
[27] [28] [29] Jia L Q,Zhang Y Y,Zheng S W 2007 Journal of Ynunan University 29 589 (in Chinese) [贾利群,张耀宇,郑世旺 2007 云南大学学报 29 589]
[30] 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]
[31] [32] 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]
[33] [34] 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]
[35] [36] [37] Yang X F,Jia L Q,Cui J C,Luo S K 2010 Chin.Phys.B 19 030305
[38] [39] Jia L Q,Xie J F,Luo S K 2008 Chin.Phys.B 17 1560
[40] [41] Cai J L 2009 Acta Phys.Sin.58 22 (in Chinese) [蔡建乐 2009 58 22]
[42] Djukic D S,Vujanovic B 1975 Acta Mechanica 23 17
[43] [44] Bahar L Y,Kwatry H G 1987 Int.J.Non-Linear Mech.22 125
[45] [46] [47] Li Z P 1981 Acta Phys.Sin.20 1659 (in Chinese) [李子平 1981 20 1659]
[48] Li Z P 1991 J.Phys.A:Math.Gen.24 4261
[49] [50] Li Z P 1993 Classical and Quantum Constrained Systems and Symmetry (Beijing:Beijing industrial university Press) (in Chinese)[李子平 1993 经典和量子约束系统及其对称性质(北京:北京工业大学出版社)]
[51] [52] [53] Dong W S,Huang B X,Fang J H 2011 Chin.Phys.B 20 010204
[54] [55] Xia L L,Shan L F 2010 Chin.Phys.B 19 090302
[56] Luo S K 2007 Chin.Phys.16 3182
[57] [58] [59] Shi Y,Fu R,Ma S J 2007 Journal of University of Science and Technology of Suzhou (Natural Science Edition) 24 34 (in Chinese)[施勇,傅蓉,马善钧 2007 苏州科技学院学报 (自然科学版) 24 34]
[60] [61] Ma S J,Liu M P,Huang P T 2005 Chin.Phys.14 244
[62] Mei F X,Shui X P 2006 Journal of Beijing Institute of Technology 26 285 (in Chinese) [梅凤翔,水小平 2006 北京理工大学学报 26 285]
[63] [64] [65] Mei F X 1985 Foundations of Mechanics of Nonholonomic Systems(Beijing:Beijing Institute of Industrial 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)]
[66] 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)]
[67]
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