变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量

杨新芳; 孙现亭; 王肖肖; 张美玲; 贾利群

doi:10.7498/aps.60.111101

摘要

研究变质量Chetaev型非完整系统Appell方程的Mei对称性和Mei守恒量.建立变质量Chetaev型非完整系统的Appell方程和系统的运动微分方程; 给出函数沿系统运动轨道曲线对时间t全导数的表示式,并在群的无限小变换下,给出变质量Chetaev型非完整系统Appell方程Mei对称性的定义和判据;得到用Appell函数表示的Mei对称性的结构方程和Mei守恒量的表达式,并举例说明结果的应用.

关键词:

Abstract

Mei symmetry and Mei conserved quantity of Appell equation for a nonholonomic system of Chetaevs type with variable mass are studied. The Appell equation and differential equation of motion of the system are set up. The expression of the total derivative of the function along the trajectory of the system with respect to t, the definition and criterion of Mei symmetry of Appell equation for a nonholonomic system of Chetaevs type with variable mass under the infinitesimal transformation of group are given. The structural equation of Mei symmetry and the expression of Mei conserved quantity expressed by Appell equation are obtained. An example is given to illustrate the application of the results.

Keywords:

作者及机构信息

1.
江南大学理学院,无锡 214122;

2.
平顶山学院电气信息工程学院,平顶山 467002

基金项目: 中央高校基本科研业务费专项基金(批准号: JUSRP31102)和国家自然科学基金(批准号:61178032)资助的课题.

Authors and contacts

1.
School of Science, Jiangnan University, Wuxi 214122, China;

2.
Electric and Information Engineering College, Pingdingshan University, Pingdingshan 467002, China

参考文献

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[2]	Noether A E 1918 Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl, II 235
[3]	Vujanovi Ac' B 1986 Acta Mech. 65 63
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[8]	Ge W K, Mei F X 2009 Acta Phys. Sin. 58 699(in Chinese)[葛伟宽、梅凤翔 2009 58 699]
[9]	Zhang Y 2008 Chin. Phys. B 17 4365
[10]	Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese)[罗绍凯、张永发 2008 约束系统动力学研究进展(北京:科学出版社)]
[11]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[12]	Cai J L 2009 Acta Phys. Sin. 58 22(in Chinese)[蔡建乐 2009 58 22]
[13]	Fang J H 2010 Chin. Phys. B 19 040301
[14]	Luo S K, Guo Y X 2007 Commun. Theor. Phys. 47 25
[15]	Jia L Q, Zhang Y Y,Yang X F,Cui J C, Xie Y L 2010 Acta Phys. Sin. 59 2939 (in Chinese)[贾利群、张耀宇、杨新芳、崔金超、解银丽 2010 59 2939]
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[17]	Mei F X 1985 Foundations of mechanics of nonholonomic systems (Beijing: Beijing Institute of Technology Press) 214 (in Chinese) [梅凤翔 1985 非完整系统力学基础(北京:北京工业学院出版社)214]
[18]	Mei F X 2001 Chin. Phys. 10 117
[19]	Luo S K 2002 Acta Phys. Sin. 51 712(in Chinese) [罗绍凯 2002 51 712]
[20]	Jia L Q, Zhang Y Y, Cui J C, Luo S K 2009 Commun. Theor. Phys. 52 572
[21]	Li Y C, Xia L L,Wang X M, Liu X W 2010 Acta Phys.Sin. 59 3639 (in Chinese)[李元成、夏丽莉、王小明、刘晓巍 2010 59 3639]
[22]	Jia L Q, Xie Y L, Zhang Y Y, Cui J C,Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese)[贾利群、解银丽、张耀宇、崔金超、杨新芳 2010 59 7552]
[23]	Xie Y L, Jia L Q 2010 Chin. Phys. Lett. 27 120201
[24]	Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
[25]	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]
[26]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing:Beijing Institute of Technology Press)168 (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)168]
[27]	Chen X W, Mei F X 2000 Chin. Phys. 9 721
[28]	Li R J, Qiao Y F, Meng J 2002 Acta Phys. Sin. 51 1(in Chinese)[李仁杰、乔永芬、孟军 2002 51 1]
[29]	Mei F X 2003 Trans. Beijing Inst. Technol. 23 1(in Chinese) [梅凤翔2003 北京理工大学学报 23 1]
[30]	Fang J H 2003 Commun. Theor. Phys. 40 269

施引文献

[1]	Appell P 1899 C. R. cad. Sc. Paris 129 317
[2]	Noether A E 1918 Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl, II 235
[3]	Vujanovi Ac' B 1986 Acta Mech. 65 63
[4]	Mei F X 2001 J.Beijing Institute of Tech. 21 535 (in Chinese)[梅凤翔 2001 北京理工大学学报 21 535]
[5]	Mei F X 2003 Acta Phys. Sin. 52 1048(in Chinese) [梅凤翔 2003 52 1048]
[6]	Luo S K 2007 Acta Phys. Sin. 56 5580 (in Chinese) [罗绍凯 2007 56 5580]
[7]	Luo S K,Chen X W, Guo Y X 2007 Chin. Phys. 16 3176
[8]	Ge W K, Mei F X 2009 Acta Phys. Sin. 58 699(in Chinese)[葛伟宽、梅凤翔 2009 58 699]
[9]	Zhang Y 2008 Chin. Phys. B 17 4365
[10]	Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese)[罗绍凯、张永发 2008 约束系统动力学研究进展(北京:科学出版社)]
[11]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[12]	Cai J L 2009 Acta Phys. Sin. 58 22(in Chinese)[蔡建乐 2009 58 22]
[13]	Fang J H 2010 Chin. Phys. B 19 040301
[14]	Luo S K, Guo Y X 2007 Commun. Theor. Phys. 47 25
[15]	Jia L Q, Zhang Y Y,Yang X F,Cui J C, Xie Y L 2010 Acta Phys. Sin. 59 2939 (in Chinese)[贾利群、张耀宇、杨新芳、崔金超、解银丽 2010 59 2939]
[16]	Jia L Q, Xie Y L, Zhang Y Y, Yang X F 2010 Chin. Phys. B 19 110301
[17]	Mei F X 1985 Foundations of mechanics of nonholonomic systems (Beijing: Beijing Institute of Technology Press) 214 (in Chinese) [梅凤翔 1985 非完整系统力学基础(北京:北京工业学院出版社)214]
[18]	Mei F X 2001 Chin. Phys. 10 117
[19]	Luo S K 2002 Acta Phys. Sin. 51 712(in Chinese) [罗绍凯 2002 51 712]
[20]	Jia L Q, Zhang Y Y, Cui J C, Luo S K 2009 Commun. Theor. Phys. 52 572
[21]	Li Y C, Xia L L,Wang X M, Liu X W 2010 Acta Phys.Sin. 59 3639 (in Chinese)[李元成、夏丽莉、王小明、刘晓巍 2010 59 3639]
[22]	Jia L Q, Xie Y L, Zhang Y Y, Cui J C,Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese)[贾利群、解银丽、张耀宇、崔金超、杨新芳 2010 59 7552]
[23]	Xie Y L, Jia L Q 2010 Chin. Phys. Lett. 27 120201
[24]	Xie Y L, Jia L Q, Luo S K 2011 Chin. Phys. B 20 010203
[25]	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]
[26]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing:Beijing Institute of Technology Press)168 (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)168]
[27]	Chen X W, Mei F X 2000 Chin. Phys. 9 721
[28]	Li R J, Qiao Y F, Meng J 2002 Acta Phys. Sin. 51 1(in Chinese)[李仁杰、乔永芬、孟军 2002 51 1]
[29]	Mei F X 2003 Trans. Beijing Inst. Technol. 23 1(in Chinese) [梅凤翔2003 北京理工大学学报 23 1]
[30]	Fang J H 2003 Commun. Theor. Phys. 40 269

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