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研究Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量. 对Chetaev型约束的相对运动力学系统Nielsen方程的运动微分方程、Noether对称性定义和判据进行具体的研究, 得到了Noether对称性直接导致的Noether守恒量的表达式. 最后举例说明结果的应用.
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关键词:
- Chetaev型约束 /
- 相对运动动力学 /
- Nielsen方程 /
- Noether守恒量
[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 物理学报 53 2419]
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[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]
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[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 物理学报 59 5209]
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[42] Djukic D S,Vujanovic B 1975 Acta Mechanica 23 17
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[48] Li Z P 1991 J.Phys.A:Math.Gen.24 4261
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[54] [55] Xia L L,Shan L F 2010 Chin.Phys.B 19 090302
[56] Luo S K 2007 Chin.Phys.16 3182
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[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]
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[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 物理学报 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 物理学报 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 物理学报 58 16]
[22] Mei F X,Shang M 2000 Acta Phys.Sin.49 1901 (in Chinese) [梅凤翔,尚玫 2000 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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