【摘要】 首先将 n维未知向量 q的二阶非线性动力系统 Mq..+Gq.+Kq=F(q.,q,t)转化为与其等价的2 n维未知向量 v的一阶微分方程 v.=H v +f(v,t) ,其中非线性部分 fi(v,t) =0 (i=1 ,… ,n) ,fi(v,t) =Fi-n(q.,q,t) (i=n+ 1 ,… ,2 n) ;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。更多还原

【Abstract】 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.更多还原