2004 42 (03): 443-452   ISSN: 0253-6102  CN: 11-2592/O3   
 
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· LUO Xu-Dong,1 GUO Han-Ying,2 LI Yu-Qi,2 and WU Ke3
Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
LUO Xu-Dong,1 GUO Han-Ying,2 LI Yu-Qi,2 and WU Ke3

1 Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
2 Institute of Theoretical Physics, the Chinese Academia of Sciences, P.O. Box 2735, Beijing 100080, China
3 Department of Mathematics, Capital Normal University, Beijing 100037, China
Received 2004-1-2 Revised Online Accepted
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 symplecticity 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.

Key words   discrete mechanics   symplectic algorithm   variational principle  
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