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

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

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.

Keywords: 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

Received: 13 February 2014
Revised: 31 March 2014
Accepted manuscript online:

PACS:

45.20.Jj

(Lagrangian and Hamiltonian mechanics)

Fund: Project supported by the Science and Technology Program of Xi'an City, China (Grant No. CXY1352WL34).

Corresponding Authors: Zhang Xiang-Wu
E-mail: zhxw0215@aliyun.com

About author: 45.20.Jj

Cite this article:

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 2014 Chin. Phys. B 23 104501


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[1]	Symmetry of Lagrangians of holonomic nonconservative system in event space Zhang Bin(张斌), Fang Jian-Hui(方建会), and Zhang Wei-Wei(张伟伟) . Chin. Phys. B, 2012, 21(7): 070208.
[2]	Poisson theory and integration method of Birkhoffian systems in the event space Zhang Yi(张毅). Chin. Phys. B, 2010, 19(8): 080301.
[3]	Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space Zhang Yi(张毅) . Chin. Phys. B, 2009, 18(11): 4636-4642.
[4]	Routh method of reduction for Birkhoffian systems in the event space Zhang Yi (张毅). Chin. Phys. B, 2008, 17(12): 4365-4368.
[5]	Unified symmetry of the nonholonomic system of non-Chetaev type with unilateral constraints in event space Hou Qi-Bao(后其宝), Li Yuan-Cheng(李元成), Wang Jing(王静), and Xia Li-Li(夏丽莉). Chin. Phys. B, 2007, 16(6): 1521-1525.
[6]	Hojman conserved quantity for nonholonomic systems of unilateral non-Chetaev type in the event space Jia Li-Qun(贾利群), Zhang Yao-Yu(张耀宇), and Luo Shao-Kai(罗绍凯). Chin. Phys. B, 2007, 16(11): 3168-3175.
[7]	Discrete variational principle and the first integrals of the conservative holonomic systems in event space Zhang Hong-Bin (张宏彬), Chen Li-Qun (陈礼群), Liu Rong-Wan (刘荣万). Chin. Phys. B, 2005, 14(5): 888-892.

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