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题名: On variations in discrete mechanics and field theory
作者: Guo, HY ;  Wu, K
刊名: JOURNAL OF MATHEMATICAL PHYSICS
出版日期: 2003
卷号: 44, 期号:12, 页码:5978-6004
关键词: EULER-LAGRANGE COHOMOLOGY ;  NONCOMMUTATIVE DIFFERENTIAL-CALCULUS ;  MULTISYMPLECTIC STRUCTURES ;  INTEGRATORS ;  PRINCIPLES ;  FORMALISM ;  VERSIONS
学科分类: Physics
通讯作者: Guo, HY , China Ctr Adv Sci & Technol, POB 8730, Beijing 100080, Peoples R China.
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
英文摘要: 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.
收录类别: SCI
原文出处: 查看原文
WOS记录号: WOS:000186662300027
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/14166
Appears in Collections:理论物理所1978-2010年知识产出_期刊论文

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Recommended Citation:
Guo, HY,Wu, K. On variations in discrete mechanics and field theory[J]. JOURNAL OF MATHEMATICAL PHYSICS,2003,44(12):5978-6004.
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