六自由度外弹道方程组的快速数值方法  

A FAST NUMERICAL METHOD FOR THE SIX DEGREES OF FREEDOM MODEL IN THE EXTERNAL BALLISTICS

作　　者：杨青[1] 李若[2] 蔡振宁[2] 

机构地区：[1]中国船舶工业集团公司船舶系统工程部 [2]北京大学数学科学学院

出　　处：《高等学校计算数学学报》2014年第3期253-270,共18页Numerical Mathematics A Journal of Chinese Universities

摘　　要：This paper concentrates on the numerical solution of the exterior trajectory of grenades.We consider the model with six degrees of freedom,which is an initial value problem of an ordinary differential system with twelve variables.Due to the high oscillating property of the equations,only very small time steps must be used when the explicit Runge-Kutta methods are applied,which leads to an unsatisfying efficiency.In this paper,we use the skill of asymptotic expansion to obtain the analytical expressions of the approximate solutions of two variables.Thus the oscillations in the solutions are significantly reduced,and the time step can be enlarged intrinsically.Numerical examples show that the efficiency is effectively enhanced by this method.This paper concentrates on the numerical solution of the exterior tra- jectory of grenades. We consider the model with six degrees of freedom, which is an initial value problem of an ordinary differential system with twelve variables. Due to the high oscillating property of the equations, only very small time steps must be used when the explicit Runge-Kutta methods are applied, which leads to an unsatisfying efficiency. In this paper, we use the skill of asymptotic expansion to obtain the analytical expressions of the approximate solutions of two variables. Thus the oscillations in the solutions are significantly reduced, and the time step can be enlarged intrinsically. Numerical examples show that the efficiency is effec- tively enhanced by this method.

关 键 词：弹道方程组 六自由度 数值方法 舰炮系统 模型描述 海上战争 命中概率 空间坐标 

分 类 号：O24[理学—计算数学] O29[理学—数学]