Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

doi:10.1088/1674-1056/23/10/104501

中国物理B ›› 2014, Vol. 23 ›› Issue (10): 104501-104501.doi: 10.1088/1674-1056/23/10/104501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

张相武^a, 李院院^a, 赵小侠^a, 罗文峰^b

a School of Physics and Mechatronic Engineering, Xi'an University of Arts and Science, Xi'an 710065, China;
b School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China

收稿日期:2014-02-13 修回日期:2014-03-31 出版日期:2014-10-15 发布日期:2014-10-15
基金资助:
Project supported by the Science and Technology Program of Xi'an City, China (Grant No. CXY1352WL34).

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

Zhang Xiang-Wu (张相武)^a, Li Yuan-Yuan (李院院)^a, Zhao Xiao-Xia (赵小侠)^a, Luo Wen-Feng (罗文峰)^b

a School of Physics and Mechatronic Engineering, Xi'an University of Arts and Science, Xi'an 710065, China;
b School of Electronic Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China

Received:2014-02-13 Revised:2014-03-31 Online:2014-10-15 Published:2014-10-15
Contact: Zhang Xiang-Wu E-mail:zhxw0215@aliyun.com
About author:45.20.Jj
Supported by:
Project supported by the Science and Technology Program of Xi'an City, China (Grant No. CXY1352WL34).

摘要/Abstract

摘要： In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert-Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.

关键词: event space, the higher-order d’, Alembert-Lagrange principle, the higher-order time rate of change of force, the higher-order differential equations of motion

Abstract: In this paper we study the higher-order differential variational principle and differential equations of motion for mechanical systems in event space. Based on the higher-order d'Alembert principle of the system, the higher-order velocity energy and the higher-order acceleration energy of the system in event space are defined, the higher-order d'Alembert-Lagrange principle of the system in event space is established, and the parametric forms of Euler-Lagrange, Nielsen and Appell for this principle are given. Finally, the higher-order differential equations of motion for holonomic systems in event space are obtained.

Key words: event space, the higher-order d’, Alembert-Lagrange principle, the higher-order time rate of change of force, the higher-order differential equations of motion

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

张相武, 李院院, 赵小侠, 罗文峰. Higher-order differential variational principle and differential equations of motion for mechanical systems in event space[J]. 中国物理B, 2014, 23(10): 104501-104501.

Zhang Xiang-Wu (张相武), Li Yuan-Yuan (李院院), Zhao Xiao-Xia (赵小侠), Luo Wen-Feng (罗文峰). Higher-order differential variational principle and differential equations of motion for mechanical systems in event space[J]. Chin. Phys. B, 2014, 23(10): 104501-104501.

参考文献 0


[1]	Synge J L 1960 Classical Dynamics (Berlin: Springer-Verlag)

[2]	Rumyantsev V V 1983 Proceedings of the IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics (Torino: Science Press)

[3]	Mei F X 1988 Acta Mech. Sin. 20 557 (in Chinese)

[4]	Mei F X 1988 Acta Armamentarii 9 27 (in Chinese)

[5]	Mei F X 1990 Acta Mech. Sin. 6 160 doi: 10.1007/BF02488447

[6]	Mei F X, Liu D and Luo Y 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese)

[7]	Mei F X 1988 J. Beijing Inst. Technol. 8 22 (in Chinese)

[8]	Luo S K 1991 J. Natural Science of Chengdu University 10 30 (in Chinese)

[9]	Luo S K 1992 J. Tianjin Educational Institute 1 12 (in Chinese)

[10]	Luo S K 1992 J. Inner Mongolia Normal University 21 29 (in Chinese)

[11]	Luo S K 1993 J. Guangxi University 18 52 (in Chinese)

[12]	Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 14 888 doi: 10.1088/1009-1963/14/5/005

[13]	Zhang Y 2007 Acta Phys. Sin. 56 655 (in Chinese)

[14]	Zhang Y 2008 Acta Phys. Sin. 57 2649 (in Chinese)

[15]	Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)

[16]	Mei F X 2003 J. Jiangxi Normal University 27 1 (in Chinese)

[17]	Mei F X 2004 Symmetry and Conserved Quantity of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)

[18]	Li Y C, Zhang Y and Liang J H 2000 Appl. Math. Mech. 21 543 doi: 10.1007/BF02459035

[19]	Li Y C, Liang J H, Zhang Y and Mei F X 2000 J. Beijing Inst. Technol. 20 21 (in Chinese)

[20]	Li Y C, Zhang Y and Liang J H 2001 Acta Mech. Solida Sin. 22 75 (in Chinese)

[21]	Xu X J, Mei F X and Qin M C 2005 Acta Phys. Sin. 54 1009 (in Chinese)

[22]	Zhang Y 2007 Acta Phys. Sin. 56 3054 (in Chinese)

[23]	Zhang Y 2008 Acta Phys. Sin. 57 2643 (in Chinese)

[24]	Zhang Y 2008 Commun. Theor. Phys. 50 59 doi: 10.1088/0253-6102/50/1/12

[25]	Zhang Y 2009 Chin. Phys. B 18 4636

[26]	Zhang Y 2010 Commun. Theor. Phys. 53 166 doi: 10.1088/0253-6102/53/1/34

[27]	Jia L Q, Zhang Y Y and Zheng S W 2007 Acta Phys. Sin. 56 649 (in Chinese)

[28]	Jia L Q, Zheng S W and Zhang Y Y 2007 Acta Phys. Sin. 56 5575 (in Chinese)

[29]	Jia L Q, Luo S K and Zhang Y Y 2007 Acta Phys. Sin. 56 6188 (in Chinese)

[30]	Jia L Q, Zhang Y Y and Luo S K 2007 Chin. Phys. 16 3168 doi: 10.1088/1009-1963/16/11/004

[31]	Jia L Q, Zhang Y Y, Luo S K and Cui J C 2009 Acta Phys. Sin. 58 2141 (in Chinese)

[32]	Hou Q B, Li Y C, Wang J and Xia L L 2007 Chin. Phys. 16 1521 doi: 10.1088/1009-1963/16/6/005

[33]	Hou Q B, Li Y C, Xia L L and Wang J 2007 Commun. Theor. Phys. 48 619 doi: 10.1088/0253-6102/48/4/008

[34]	Hou Q B, Li Y C, Wang J and Xia L L 2007 Commun. Theor. Phys. 48 795 doi: 10.1088/0253-6102/48/5/006

[35]	Zhang B, Fang J H and Zhang W W 2012 Chin. Phys. B 21 070208

[36]	Ma S J, Xu X X, Huang P T and Hu L Y 2004 Acta Phys. Sin. 53 3648 (in Chinese)

[37]	Ma S J, Liu M P and Huang P T 2005 Chin. Phys. 14 244 doi: 10.1088/1009-1963/14/2/004

[38]	Ma S J, Ge W G and Huang P T 2005 Chin. Phys. 14 879 doi: 10.1088/1009-1963/14/5/003

[39]	Ma S J, Huang P T, Yan R and Zhao H X 2006 Chin. Phys. 15 2193 doi: 10.1088/1009-1963/15/10/001

[40]	Ma S J, Yang X H, Yan R and Huang P T 2006 Commun. Theor. Phys. 45 350 doi: 10.1088/0253-6102/45/2/031

[41]	Ma S J, Yang X H and Yan R 2006 Commun. Theor. Phys. 46 309 doi: 10.1088/0253-6102/46/2/026

[42]	Yang X H and Ma S J 2006 Chin. Phys. 15 1672 doi: 10.1088/1009-1963/15/8/005

[43]	Zhang X W 2005 Acta Phys. Sin. 54 3978 (in Chinese)

[44]	Zhang X W 2005 Acta Phys. Sin. 54 4483 (in Chinese)

[45]	Zhang X W 2006 Acta Phys. Sin. 55 1543 (in Chinese)

[46]	Zhang X W 2006 Acta Phys. Sin. 55 2669 (in Chinese)

[47]	Shi Y 2006 Acta Phys. Sin. 55 4991 (in Chinese)

[48]	Zhao H X and Ma S J 2008 Commun. Theor. Phys. 49 297 doi: 10.1088/0253-6102/49/2/08

[49]	Zhao H X, Ma S J and Shi Y 2008 Commun. Theor. Phys. 49 479 doi: 10.1088/0253-6102/49/2/47

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 0

相关文章 5

Metrics

本文评价

推荐阅读 0

[1]	张斌, 方建会, 张伟伟 . Symmetry of Lagrangians of holonomic nonconservative system in event space[J]. 中国物理B, 2012, 21(7): 70208-070208.
[2]	张毅. Poisson theory and integration method of Birkhoffian systems in the event space[J]. 中国物理B, 2010, 19(8): 80301-080301.
[3]	张毅. Routh method of reduction for Birkhoffian systems in the event space[J]. 中国物理B, 2008, 17(12): 4365-4368.
[4]	后其宝, 李元成, 王静, 夏丽莉. Unified symmetry of the nonholonomic system of non-Chetaev type with unilateral constraints in event space[J]. 中国物理B, 2007, 16(6): 1521-1525.
[5]	张宏彬, 陈礼群, 刘荣万. Discrete variational principle and the first integrals of the conservative holonomic systems in event space　　　　　[J]. 中国物理B, 2005, 14(5): 888-892.