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Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm | | Xu-Dong Luo
; Han-Ying Guo
; Yu-Qi Li
; Ke Wu
; | | Date: |
8 Oct 2004 | | Journal: | Comm. Theor. Phys., 42, 443-452, (2004) | | Subject: | Mathematical Physics | math-ph math.MP | | Abstract: | We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This approach keeps both symplicticity and energy conservation discretely. We show that there exists the discrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existence in finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodic perturbation. The numerical results are satisfactory. | | Source: | arXiv, math-ph/0410024 | | Services: | Forum | Review | PDF | Favorites | |
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