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

变质量非完整系统Tznoff方程的Lie 对称性与其导出的守恒量

郑世旺 王建波 陈向炜 李彦敏 解加芳

引用本文:
Citation:

变质量非完整系统Tznoff方程的Lie 对称性与其导出的守恒量

郑世旺, 王建波, 陈向炜, 李彦敏, 解加芳

Lie symmetry and their conserved quantities of Tznoff equations for the vairable mass nonholonomic systems

Zheng Shi-Wang, Wang Jian-Bo, Chen Xiang-Wei, Li Yan-Min, Xie Jia-Fang
PDF
导出引用
  • 航天器运行系统大都属于变质量力学系统, 变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律. 本文首先导出了变质量非完整力学系统的Tznoff方程, 然后研究了变质量非完整力学系统Tznoff方程的Lie对称性及其所导出的守恒量, 给出了这种守恒量的函数表达式和导出这种守恒量的判据方程. 该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.
    The operational system of the spacecraft is general a variable mass one, of which the symmetry and the conserved quantity imply physical rules of the space system. In this paper, Tznoff equations of the variable mass nonholonomic system are derived, from which the Lie symmetries of Tznoff equations for the variable mass nonholonomic system and conserved quantities are derived and are researched. The function expressions of conserved quantities and the criterion equations which deduce these conserved quantities are presented. This result has some theoretical value for further research of the conservation laws obeyed by the variable mass system.
    • 基金项目: 国家自然科学基金(批准号: 10972127, 11102001) 资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10972127, 11102001).
    [1]

    Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI II 235

    [2]

    Li Z P 1993 Classical and Quantum Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing: Beijing Polytechnic University Press) p5 (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) 第5页]

    [3]
    [4]
    [5]

    Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p90 (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) 第90页]

    [6]
    [7]

    Mei F X 2000 J. Beijing Inst. Technol. 9 120

    [8]

    Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) p264 (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) 第264页]

    [9]
    [10]
    [11]

    Fu J L, Chen L Q, Xie F P 2004 Chin. Phys. 13 1611

    [12]

    Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470

    [13]
    [14]

    Luo S K 2007 Chin. Phys. 16 3182

    [15]
    [16]
    [17]

    Wu H B, Mei F X 2010 Chin. Phys. B 19 030303

    [18]

    Zhang Y 2008 Commun. Theor. Phys. 50 59

    [19]
    [20]

    Lou Z M 2010 Acta Phys. Sin. 59 719 (in Chinese) [楼智美 2010 物理学报 59 719]

    [21]
    [22]
    [23]

    Xia L L 2011 Chin. Phys. Lett. 28 040201

    [24]

    Liu X W, Li Y C, Xia L L 2011 Chin. Phys. B 20 070203

    [25]
    [26]

    Zhang H B, Chen L Q, Gu S L 2004 Commun. Theor. Phys. 42 321

    [27]
    [28]
    [29]

    Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 物理学报 58 3617]

    [30]

    Fang J H 2010 Chin. Phys. B 19 040301

    [31]
    [32]

    Li Y, Fang J H, Zhang K J 2011 Chin. Phys. B 20 030201

    [33]
    [34]

    Jia L Q, Xie Y L, Luo S K 2011 Acta Phys. Sin. 60 040201 (in Chinese) [贾利群, 解银丽, 罗绍凯 2011 物理学报 60 040201]

    [35]
    [36]

    Xie Y, Jia L Q 2010 Chin. Phys. Lett. 27 120201

    [37]
    [38]

    Ding N, Fang J H 2011 Chin. Phys. B 20 120201

    [39]
    [40]
    [41]

    Wang P 2011 Chin. Phys. Lett. 28 040203

    [42]
    [43]

    Zheng S W, Jia L Q, Yu H S 2006 Chin. Phys. 15 1399

    [44]

    Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809

    [45]
    [46]

    Zheng S W, Xie J F, Jia L Q 2007 Commun. Theor. Phys. 48 43

    [47]
    [48]
    [49]

    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]

    [50]

    Zheng S W, Xie J F, Wang J B, Chen X W 2010 Chin. Phys. Lett. 27 030307

    [51]
    [52]
    [53]

    Chen X W, Mei F X 2000 Chin. Phys. 9 721

    [54]

    Mei F X 2003 Tr Beijing Inst. Technol. 23 1 (in Chinese) [梅凤翔2003 北京理工大学学报 23 1]

    [55]
    [56]

    Fang J H 2003 Commun. Theor. Phys. 40 269

    [57]
    [58]
    [59]

    Zhang P Y, Fang J H 2006 Acta Phys. Sin. 55 3813 (in Chinese) [张鹏玉, 方建会 2006 物理学报 55 3813]

    [60]
    [61]

    Mei F X, Liu D, Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) p339 (in Chinese) [梅凤翔, 刘端, 罗 勇 1991 高等分析力学 (北京: 北京理工大学出版社) 第339页]

  • [1]

    Noether A E 1918 Nachr. Akad. Wiss. Gttingen. Math. Phys. KI II 235

    [2]

    Li Z P 1993 Classical and Quantum Dynamics of Constrained Systems and Their Symmetrical Properties (Beijing: Beijing Polytechnic University Press) p5 (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) 第5页]

    [3]
    [4]
    [5]

    Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) p90 (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) 第90页]

    [6]
    [7]

    Mei F X 2000 J. Beijing Inst. Technol. 9 120

    [8]

    Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) p264 (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) 第264页]

    [9]
    [10]
    [11]

    Fu J L, Chen L Q, Xie F P 2004 Chin. Phys. 13 1611

    [12]

    Chen X W, Liu C M, Li Y M 2006 Chin. Phys. 15 470

    [13]
    [14]

    Luo S K 2007 Chin. Phys. 16 3182

    [15]
    [16]
    [17]

    Wu H B, Mei F X 2010 Chin. Phys. B 19 030303

    [18]

    Zhang Y 2008 Commun. Theor. Phys. 50 59

    [19]
    [20]

    Lou Z M 2010 Acta Phys. Sin. 59 719 (in Chinese) [楼智美 2010 物理学报 59 719]

    [21]
    [22]
    [23]

    Xia L L 2011 Chin. Phys. Lett. 28 040201

    [24]

    Liu X W, Li Y C, Xia L L 2011 Chin. Phys. B 20 070203

    [25]
    [26]

    Zhang H B, Chen L Q, Gu S L 2004 Commun. Theor. Phys. 42 321

    [27]
    [28]
    [29]

    Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 物理学报 58 3617]

    [30]

    Fang J H 2010 Chin. Phys. B 19 040301

    [31]
    [32]

    Li Y, Fang J H, Zhang K J 2011 Chin. Phys. B 20 030201

    [33]
    [34]

    Jia L Q, Xie Y L, Luo S K 2011 Acta Phys. Sin. 60 040201 (in Chinese) [贾利群, 解银丽, 罗绍凯 2011 物理学报 60 040201]

    [35]
    [36]

    Xie Y, Jia L Q 2010 Chin. Phys. Lett. 27 120201

    [37]
    [38]

    Ding N, Fang J H 2011 Chin. Phys. B 20 120201

    [39]
    [40]
    [41]

    Wang P 2011 Chin. Phys. Lett. 28 040203

    [42]
    [43]

    Zheng S W, Jia L Q, Yu H S 2006 Chin. Phys. 15 1399

    [44]

    Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809

    [45]
    [46]

    Zheng S W, Xie J F, Jia L Q 2007 Commun. Theor. Phys. 48 43

    [47]
    [48]
    [49]

    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]

    [50]

    Zheng S W, Xie J F, Wang J B, Chen X W 2010 Chin. Phys. Lett. 27 030307

    [51]
    [52]
    [53]

    Chen X W, Mei F X 2000 Chin. Phys. 9 721

    [54]

    Mei F X 2003 Tr Beijing Inst. Technol. 23 1 (in Chinese) [梅凤翔2003 北京理工大学学报 23 1]

    [55]
    [56]

    Fang J H 2003 Commun. Theor. Phys. 40 269

    [57]
    [58]
    [59]

    Zhang P Y, Fang J H 2006 Acta Phys. Sin. 55 3813 (in Chinese) [张鹏玉, 方建会 2006 物理学报 55 3813]

    [60]
    [61]

    Mei F X, Liu D, Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) p339 (in Chinese) [梅凤翔, 刘端, 罗 勇 1991 高等分析力学 (北京: 北京理工大学出版社) 第339页]

  • [1] 徐超, 李元成. 奇异 Chetaev型非完整系统Nielsen方程的Lie-Mei对称性与守恒量. 物理学报, 2013, 62(12): 120201. doi: 10.7498/aps.62.120201
    [2] 张斌, 方建会, 张克军. 变质量非完整系统的Lagrange对称性与守恒量. 物理学报, 2012, 61(2): 021101. doi: 10.7498/aps.61.021101
    [3] 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
    [4] 郑世旺, 解加芳, 陈向炜, 杜雪莲. 完整系统Tzénoff方程的Mei对称性直接导致的另一种守恒量. 物理学报, 2010, 59(8): 5209-5212. doi: 10.7498/aps.59.5209
    [5] 李元成, 王小明, 夏丽莉. 完整系统Nielsen方程的统一对称性与守恒量. 物理学报, 2010, 59(5): 2935-2938. doi: 10.7498/aps.59.2935
    [6] 李元成, 夏丽莉, 王小明, 刘晓巍. 完整系统Appell方程的Lie-Mei对称性与守恒量. 物理学报, 2010, 59(6): 3639-3642. doi: 10.7498/aps.59.3639
    [7] 蔡建乐. 一般完整系统Mei对称性的共形不变性与守恒量. 物理学报, 2009, 58(1): 22-27. doi: 10.7498/aps.58.22
    [8] 张毅, 葛伟宽. 非Chetaev型非完整系统的Lagrange对称性与守恒量. 物理学报, 2009, 58(11): 7447-7451. doi: 10.7498/aps.58.7447
    [9] 张毅. 广义Birkhoff系统的Birkhoff对称性与守恒量. 物理学报, 2009, 58(11): 7436-7439. doi: 10.7498/aps.58.7436
    [10] 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
    [11] 蔡建乐, 梅凤翔. Lagrange系统Lie点变换下的共形不变性与守恒量. 物理学报, 2008, 57(9): 5369-5373. doi: 10.7498/aps.57.5369
    [12] 刘仰魁, 方建会. 相空间中变质量力学系统Lie-Mei对称性的两个守恒量. 物理学报, 2008, 57(11): 6699-6703. doi: 10.7498/aps.57.6699
    [13] 葛伟宽. 一类完整系统的Mei对称性与守恒量. 物理学报, 2008, 57(11): 6714-6717. doi: 10.7498/aps.57.6714
    [14] 郑世旺, 贾利群. 非完整系统Tzénoff方程的Mei对称性和守恒量. 物理学报, 2007, 56(2): 661-665. doi: 10.7498/aps.56.661
    [15] 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
    [16] 张毅. Birkhoff系统的一类Lie对称性守恒量. 物理学报, 2002, 51(3): 461-464. doi: 10.7498/aps.51.461
    [17] 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
    [18] 方建会, 赵嵩卿. 相对论性转动变质量系统的Lie对称性与守恒量. 物理学报, 2001, 50(3): 390-393. doi: 10.7498/aps.50.390
    [19] 乔永芬, 赵淑红. 准坐标下广义力学系统的Lie对称定理及其逆定理. 物理学报, 2001, 50(1): 1-7. doi: 10.7498/aps.50.1
    [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:  5962
  • PDF下载量:  670
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-05-11
  • 修回日期:  2012-06-05
  • 刊出日期:  2012-06-05

/

返回文章
返回