在哈密顿体系下分析非线性动力学问题

首先将ｎ维未知向量ｑ的二阶非线性力系统Ｍｑ＋Ｇｑ＋Ｋｑ＝Ｆ（ｑ，ｑ，ｔ）转化为与其等价的２ｎ维未知向量ｖ的一阶微分方程ｖ＝Ｈｖ＋ｆ（ｖ，ｔ），其中非线性部分ｊｉ（ｖ，ｔ）＝０（ｉ＝１，．．．ｎ），ｆｉ（ｖ，ｔ）＝Ｆｉ－ｎ（ｑ，ｑ，ｔ）（ｉ＝ｎ＋１，．．．２ｎ）；然后给出一种求解ｖ的逐步积分公式，从而将精细积分法进一步推广应用到非线性动力学问题。算例表明本方法的计算量较小且结果合理可靠。

Solving the problems of nonlinear dynamics based on Hamiltonian system

The second nonlinear system to be solved derived to the Hamitonian formulation dv/dt=Hv f(v,t), in which v is an unknown 2n|dimensional vector, H is a coefficient matrix, and f(v,t) is its nonlinear part. Based on 2 N type algorithm [3] , a precise time integration method with remarkable accuracy for solving such a nonlinear system is presented in this paper. The algorithm was proved highly effective for a series of numerical examples.