On variations in discrete mechanics and field theory

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	On variations in discrete mechanics and field theory
	Guo, HY; Wu, K; Guo, HY , China Ctr Adv Sci & Technol, POB 8730, Beijing 100080, Peoples R China.
	2003
发表期刊	JOURNAL OF MATHEMATICAL PHYSICS
ISSN	0022-2488
卷号	44 期号:12 页码:5978-6004
摘要	In this paper, we propose the difference variational approach with variable step-length for discrete mechanics and field theory. Based upon the Hamilton's principle for the vertical variations and the horizontal variations, we get the equation of motion and the relevant relations between the equation of motion and conservation law of the energy/energy-momentum tensor for continuous as well as for the discrete systems, respectively. For those discrete cases, these relations determine the variable step-length of the differences. In addition, by taking the double operation of vertical exterior differential on action, we show that there should exist the Euler-Lagrange cohomology for both continuous and variable step-length difference cases in general. This indicates that the necessary and sufficient condition for symplectic/multisymplectic structure preserving properties is the relevant Euler-Lagrange one-form being closed in each case. Our approach can be applied to both the Lagrangian formalism and the Hamiltonian formalism, via discrete Legendre transformation, for the difference discrete mechanics and field theory. (C) 2003 American Institute of Physics.
部门归属	China Ctr Adv Sci & Technol, Beijing 100080, Peoples R China; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China; Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China
关键词	Euler-lagrange Cohomology Noncommutative Differential-calculus Multisymplectic Structures Integrators Principles Formalism Versions
学科领域	Physics
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收录类别	SCI
WOS记录号	WOS:000186662300027
引用统计	被引频次：25[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.itp.ac.cn/handle/311006/14166
专题	理论物理所SCI论文
通讯作者	Guo, HY , China Ctr Adv Sci & Technol, POB 8730, Beijing 100080, Peoples R China.
推荐引用方式 GB/T 7714	Guo, HY,Wu, K,Guo, HY , China Ctr Adv Sci & Technol, POB 8730, Beijing 100080, Peoples R China.. On variations in discrete mechanics and field theory[J]. JOURNAL OF MATHEMATICAL PHYSICS,2003,44(12):5978-6004.
APA	Guo, HY,Wu, K,&Guo, HY , China Ctr Adv Sci & Technol, POB 8730, Beijing 100080, Peoples R China..(2003).On variations in discrete mechanics and field theory.JOURNAL OF MATHEMATICAL PHYSICS,44(12),5978-6004.
MLA	Guo, HY,et al."On variations in discrete mechanics and field theory".JOURNAL OF MATHEMATICAL PHYSICS 44.12(2003):5978-6004.

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