Knowledge Management System of Institute of Theoretical Physics, CAS
| 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 | |
| Source Publication | JOURNAL OF MATHEMATICAL PHYSICS
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| Keyword | Euler-lagrange Cohomology Noncommutative Differential-calculus Multisymplectic Structures Integrators Principles Formalism Versions |
| Abstract | 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. |
| 2003 | |
| ISSN | 0022-2488 |
| Volume | 44Issue:12Pages:5978-6004 |
| Subject Area | Physics |
| Indexed By | SCI |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.itp.ac.cn/handle/311006/14166 |
| Collection | SCI期刊论文 |
| Corresponding Author | Guo, HY , China Ctr Adv Sci & Technol, POB 8730, Beijing 100080, Peoples R China. |
| Recommended Citation 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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