Hill方程在远距离拦截中的应用

Application of Hill Equation in Long-distance Interception

提出了一种通过坐标系移动，化原系中的大相对距离为新系中的小相对距离，以减小Ｈｉｌｌ方程在大相对距离时的模型误差的方法，即当拦截器的相对距离达到某一精度许可的值ρ＿１时（定义ρ＿１为精度控制参数，例如可取ρ＿１＝５００ｋｍ），以拦截器位置为原点，建立一假想的动参考系，将拦截器在原动系中的相对运动参数转换为新系中的相对运动参数（显然在新系中的初始相对距离），从而化大相对距离为小相对距离问题，提高Ｈｉｌｌ方程的描述精度。本文给出了方法的理论分析及两个计算机仿真实例，该法确可有效地减小Ｈｉｌｌ方程在大相对距离时的模型误差，结果是令人满意的。

A method to reduce the model error of Hill equation in large relative distance case is proposed in this paper, by coordinate shifting to reduce the large relative distance of original system to a small one in new system. That is, as the relative distance of interceptor is up to ρ1 (ρ1 is defined as a controlled precision parameter, for example,ρ1= 500km) .an imaginary moving reference system with its origin at the interceptor's instantanious position is set up, thus the relative motion parameters of the interceptor in original system are translated into those in the new system (obviously the initial relative distance in the new system will be. As a result, the large distance problem becomes a small one, the describing precision of Hill equation is improved. This paper provides a theoretical analysis for this method and two examples of computer simlation.