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本文研究离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量. 构建了离散差分序列变质量Hamilton系统的差分动力学方程, 给出了离散差分序列变质量Hamilton系统差分动力学方程在无限小变 换群下的Lie对称性的确定方程和定义, 得到了离散力学系统Lie对称性导致Noether守恒量的条件及形式, 举例说明结果的应用.
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关键词:
- 离散力学 /
- Hamilton系统 /
- Lie对称性 /
- Noether守恒量
In this paper the Lie symmetry and Noether conserved quantity of a discrete difference sequence Hamilton system with variable mass are studied. Firstly, the difference dynamical equations of the discrete difference sequence Hamilton system with variable mass are built. Secondly, the determining equations and the definition of Lie symmetry for difference dynamical equations of the discrete difference sequence Hamilton system under infinitesimal transformation groups are given. Thirdly, the forms and conditions of Noether conserved quantities to which Lie symmetries will lead in a discrete mechanical system are obtained. Finally, an example is given to illustrate the application of the results.[1] Mei F X 1999 Application of Lie Groups 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)]
[2] Noether A E 1918 Math. Phys. KI II 235
[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] Fang J H 2003 Commun. Theor. Phys. 40 269
[7] 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)]
[8] Wu H B 2004 Chin. Phys. 13 589
[9] Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[10] Fu J L, Chen L Q, Jimenez S, Tang Y F 2006 Phys. Lett. A 358 5
[11] Fang J H, Ding N, Wang P 2006 Acta Phys. Sin. 55 3817 (in Chinese) [方建会, 丁宁, 王鹏 2006 55 3817]
[12] Jia L Q, Zhang Y Y, Luo S K 2007 Chin. Phys. 16 3168
[13] Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese) [楼智美 2007 56 2475]
[14] 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]
[15] Liu H J, Fu J L, Tang Y F 2007 Chin. Phys. 16 599
[16] Fang J H 2010 Chin. Phys. B 19 040301
[17] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[18] Huang X H, Zhang X B, Shi S Y 2008 Acta Phys. Sin. 57 6056 (in Chinese) [黄晓虹, 张晓波, 施沈阳 2008 57 6056]
[19] Shi S Y, Fu J L, Chen L Q 2008 Chin. Phys. B 17 385
[20] Shi S Y, Huang X H, Zhang X B, Jin L 2009 Acta Phys. Sin. 58 3625 (in Chinese) [施沈阳, 黄晓虹, 张晓波, 金立 2009 58 3625]
[21] Wang X Z, Fu H, Fu J L 2012 Chin. Phys. B 21 040201
[22] Lee T D 1983 Phys. Lett. B 122 217
[23] Lee T D 1987 J. Stat. Phys. 46 843
[24] Chen J B, Guo H Y, Wu K 2003 J. Math. Phys. 44 1688
[25] Chen J B, Guo H Y, Wu K 2006 Appl. Math. Comput. 177 226
[26] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. (Beijing, China) 37 1
[27] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. (Beijing, China) 37 129
[28] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. (Beijing, China) 37 257
[29] Levi D, Yamilov R 1997 J. Math. Phys. 38 6648
[30] Levi D, Tremblay S, Winternitz P 2000 J. Phys. A: Math. Gen. 33 8507
[31] Levi D, Tremblay S, Winternitz P 2001 J. Phys. A: Math. Gen. 34 9507
[32] Dorodnitsyn V 2001 Appl. Numer. Math. 39 307
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[1] Mei F X 1999 Application of Lie Groups 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)]
[2] Noether A E 1918 Math. Phys. KI II 235
[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] Fang J H 2003 Commun. Theor. Phys. 40 269
[7] 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)]
[8] Wu H B 2004 Chin. Phys. 13 589
[9] Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[10] Fu J L, Chen L Q, Jimenez S, Tang Y F 2006 Phys. Lett. A 358 5
[11] Fang J H, Ding N, Wang P 2006 Acta Phys. Sin. 55 3817 (in Chinese) [方建会, 丁宁, 王鹏 2006 55 3817]
[12] Jia L Q, Zhang Y Y, Luo S K 2007 Chin. Phys. 16 3168
[13] Lou Z M 2007 Acta Phys. Sin. 56 2475 (in Chinese) [楼智美 2007 56 2475]
[14] 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]
[15] Liu H J, Fu J L, Tang Y F 2007 Chin. Phys. 16 599
[16] Fang J H 2010 Chin. Phys. B 19 040301
[17] Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[18] Huang X H, Zhang X B, Shi S Y 2008 Acta Phys. Sin. 57 6056 (in Chinese) [黄晓虹, 张晓波, 施沈阳 2008 57 6056]
[19] Shi S Y, Fu J L, Chen L Q 2008 Chin. Phys. B 17 385
[20] Shi S Y, Huang X H, Zhang X B, Jin L 2009 Acta Phys. Sin. 58 3625 (in Chinese) [施沈阳, 黄晓虹, 张晓波, 金立 2009 58 3625]
[21] Wang X Z, Fu H, Fu J L 2012 Chin. Phys. B 21 040201
[22] Lee T D 1983 Phys. Lett. B 122 217
[23] Lee T D 1987 J. Stat. Phys. 46 843
[24] Chen J B, Guo H Y, Wu K 2003 J. Math. Phys. 44 1688
[25] Chen J B, Guo H Y, Wu K 2006 Appl. Math. Comput. 177 226
[26] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. (Beijing, China) 37 1
[27] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. (Beijing, China) 37 129
[28] Guo H Y, Li Y Q, Wu K, Wang S K 2002 Commun. Theor. Phys. (Beijing, China) 37 257
[29] Levi D, Yamilov R 1997 J. Math. Phys. 38 6648
[30] Levi D, Tremblay S, Winternitz P 2000 J. Phys. A: Math. Gen. 33 8507
[31] Levi D, Tremblay S, Winternitz P 2001 J. Phys. A: Math. Gen. 34 9507
[32] Dorodnitsyn V 2001 Appl. Numer. Math. 39 307
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