| 用辛算法模拟单摆的振荡 |
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| 引用本文： | 刘成保,陈玉福. 用辛算法模拟单摆的振荡[J]. 中国科学院大学学报, 2012, 0(6): 721-730. DOI: 10.7523/j.issn.2095-6134.2012.6.001 |
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| 作者姓名： | 刘成保 陈玉福 |
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| 作者单位： | 中国科学院研究生院数学科学学院, 北京 100049 |
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| 摘 要： | 从哈密尔顿体系的角度,采用辛算法求解单摆的大角度摆动难题. 构造了二阶和四阶辛格式,并在长时间的模拟中得到稳定和准确的数值解. 此外, 基于辛算法的良好性质,给出可用来估计振荡周期的近似极值点方法.
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| 关 键 词： | 辛算法 模拟 单摆 大角度 哈密尔顿 |
| 收稿时间： | 2011-07-07 |
| 修稿时间： | 2011-12-19 |
Simulation of oscillation of simple pendulum by symplectic algorithm |
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| LIU Cheng-Bao,CHEN Yu-Fu. Simulation of oscillation of simple pendulum by symplectic algorithm[J]. , 2012, 0(6): 721-730. DOI: 10.7523/j.issn.2095-6134.2012.6.001 |
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| Authors: | LIU Cheng-Bao CHEN Yu-Fu |
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| Affiliation: | School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | Simple pendulum is a classical model in both physics and mathematics and its large-angle oscillation is a difficult problem in research. We use symplectic algorithm to solve this problem from the viewpoint of Hamiltonian system instead of Newtonian system. The second- and fourth-order symplectic schemes are constructed, and the solutions are stable and accurate in long time simulation. Furthermore, based on good properties of symplectic scheme, we give an approximate-extreme point method to estimate oscillation period. |
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| Keywords: | symplectic simulation simple pendulum large angle Hamiltonian |
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