搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量

徐瑞莉 方建会 张斌

引用本文:
Citation:

离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量

徐瑞莉, 方建会, 张斌

The Noether conserved quantity of Lie symmetry for discrete difference sequence Hamilton system with variable mass

Xu Rui-Li, Fang Jian-Hui, Zhang Bin
PDF
导出引用
  • 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.
    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.
    • 基金项目: 山东省自然科学基金(批准号: ZR2011AM012)和中国石油大学 (华东) 研究生自主创新科研计划项目(批准号: 13CX06005A)资助的课题.
    • Funds: Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. ZR2011AM012), and the Postgraduate’s Innovation research Foundation of China University of Petroleum (East China) (Grant No. 13CX06005A).
    [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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

  • [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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

  • [1] 孙现亭, 张耀宇, 张芳, 贾利群. 完整系统Appell方程Lie对称性的共形不变性与Hojman守恒量. 物理学报, 2014, 63(14): 140201. doi: 10.7498/aps.63.140201
    [2] 王肖肖, 孙现亭, 张美玲, 解银丽, 贾利群. 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. 物理学报, 2012, 61(6): 064501. doi: 10.7498/aps.61.064501
    [3] 解银丽, 贾利群, 杨新芳. 相对运动动力学系统Nielsen方程的Lie对称性与Hojman守恒量. 物理学报, 2011, 60(3): 030201. doi: 10.7498/aps.60.030201
    [4] 刘畅, 赵永红, 陈向炜. 动力学系统Noether对称性的几何表示. 物理学报, 2010, 59(1): 11-14. doi: 10.7498/aps.59.11
    [5] 董文山, 黄宝歆. 广义非完整力学系统的Lie对称性与Noether守恒量. 物理学报, 2010, 59(1): 1-6. doi: 10.7498/aps.59.1
    [6] 贾利群, 崔金超, 张耀宇, 罗绍凯. Chetaev型约束力学系统Appell方程的Lie对称性与守恒量. 物理学报, 2009, 58(1): 16-21. doi: 10.7498/aps.58.16
    [7] 施沈阳, 黄晓虹, 张晓波, 金立. 离散差分变分Hamilton系统的Lie对称性与Noether守恒量. 物理学报, 2009, 58(6): 3625-3631. doi: 10.7498/aps.58.3625
    [8] 黄晓虹, 张晓波, 施沈阳. 离散差分序列变质量力学系统的Mei对称性. 物理学报, 2008, 57(10): 6056-6062. doi: 10.7498/aps.57.6056
    [9] 张 凯, 王 策, 周利斌. Nambu力学系统的Lie对称性及其守恒量. 物理学报, 2008, 57(11): 6718-6721. doi: 10.7498/aps.57.6718
    [10] 方建会, 丁 宁, 王 鹏. Hamilton系统Mei对称性的一种新守恒量. 物理学报, 2007, 56(6): 3039-3042. doi: 10.7498/aps.56.3039
    [11] 施沈阳, 傅景礼, 陈立群. 离散Lagrange系统的Lie对称性. 物理学报, 2007, 56(6): 3060-3063. doi: 10.7498/aps.56.3060
    [12] 张鹏玉, 方建会. 变质量Birkhoff系统的Lie对称性和非Noether守恒量. 物理学报, 2006, 55(8): 3813-3816. doi: 10.7498/aps.55.3813
    [13] 方建会, 丁 宁, 王 鹏. 非完整力学系统的Noether-Lie对称性. 物理学报, 2006, 55(8): 3817-3820. doi: 10.7498/aps.55.3817
    [14] 顾书龙, 张宏彬. Vacco动力学方程的Mei对称性、Lie对称性和Noether对称性. 物理学报, 2005, 54(9): 3983-3986. doi: 10.7498/aps.54.3983
    [15] 张 毅. 广义经典力学系统的对称性与Mei守恒量. 物理学报, 2005, 54(7): 2980-2984. doi: 10.7498/aps.54.2980
    [16] 方建会, 陈培胜, 张 军, 李 红. 相对论力学系统的形式不变性与Lie对称性. 物理学报, 2003, 52(12): 2945-2948. doi: 10.7498/aps.52.2945
    [17] 梅凤翔. 广义Hamilton系统的Lie对称性与守恒量. 物理学报, 2003, 52(5): 1048-1050. doi: 10.7498/aps.52.1048
    [18] 罗绍凯. Hamilton系统的Mei对称性、Noether对称性和Lie对称性. 物理学报, 2003, 52(12): 2941-2944. doi: 10.7498/aps.52.2941
    [19] 李元成, 张毅, 梁景辉. 一类非完整奇异系统的Lie对称性与守恒量. 物理学报, 2002, 51(10): 2186-2190. doi: 10.7498/aps.51.2186
    [20] 梅凤翔. 包含伺服约束的非完整系统的Lie对称性与守恒量. 物理学报, 2000, 49(7): 1207-1210. doi: 10.7498/aps.49.1207
计量
  • 文章访问数:  4952
  • PDF下载量:  528
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-03-14
  • 修回日期:  2013-04-07
  • 刊出日期:  2013-08-05

/

返回文章
返回