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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
ISSN0022-2488
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
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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.
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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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