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中国科学院大学学报 ›› 2012, Vol. ›› Issue (6): 721-730.DOI: 10.7523/j.issn.2095-6134.2012.6.001

• 数学与物理学 •    下一篇

用辛算法模拟单摆的振荡

刘成保, 陈玉福   

  1. 中国科学院研究生院数学科学学院, 北京 100049
  • 收稿日期:2011-07-07 修回日期:2011-12-19 发布日期:2012-11-15
  • 通讯作者: 刘成保

Simulation of oscillation of simple pendulum by symplectic algorithm

LIU Cheng-Bao, CHEN Yu-Fu   

  1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2011-07-07 Revised:2011-12-19 Published:2012-11-15

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.

关键词: 辛算法, 模拟, 单摆, 大角度, 哈密尔顿

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.

Key words: symplectic, simulation, simple pendulum, large angle, Hamiltonian

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