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

doi:10.7498/aps.61.111101

Abstract

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:

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).

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Cited By

[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]

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Vol. 61, Issue 11 - 2012-06-05

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