用辛算法模拟单摆的振荡(英文)

Simulation of oscillation of simple pendulum by symplectic algorithm

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.

Simple pendulum is a classical model in both physics and mathematics and its largeangle 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 approximateextreme point method to estimate oscillation period.