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

doi:10.7498/aps.61.111101

摘要

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.

关键词:

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.

Keywords:

作者及机构信息

1.
商丘师范学院物理与电气信息学院, 商丘 476000;

2.
北方工业大学理学院, 北京 100144

基金项目: 国家自然科学基金(批准号: 10972127, 11102001) 资助的课题.

Authors and contacts

1.
School of Physics and Electrical Information, Shangqiu Teachers College, Shangqiu 476000, China;

2.
College of Science, North China University of Technology, Beijing 100144, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 10972127, 11102001).

参考文献

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[56]	Fang J H 2003 Commun. Theor. Phys. 40 269
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施引文献

[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 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 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 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 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 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]

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