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Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm |
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| Authors: | LUO Xu-dong GUO Han-ying LI Yu-qi WU Ke |
| Affiliation: | Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China Institute of Theoretical Physics, the Chinese Academia of Sciences, P.O. Box 2735, Beijing 100080, China Institute of Theoretical Physics, the Chinese Academia of Sciences, P.O. Box 2735, Beijing 100080, China Department of Mathematics, Capital Normal University, Beijing 100037, China |
| Abstract: | We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory. |
| Keywords: | discrete mechanics symplectic algorithm variational principle |
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