探月飞船初次再入段纵程的解析预测方法

探月飞船升阻比较低,为实现长纵程飞行,必须采用跳跃式再入方式。在跳跃式再入轨迹在线规划或预测制导中,如何快速准确地预测初次再入段纵程是一个非常关键的问题。针对这一问题,研究提出一种解析预测方法:利用匹配渐进展开方法得到再入纵向运动方程的闭型近似解;将初次再入段轨迹分为三段,第一段采用高度作为积分自变量,并利用复合梯形公式得到纵程,第二段和第三段分别采用二次多项式来拟合阻力加速度-能量剖面,根据近似解结果反解出多项式系数,并将得到的阻力加速度倒数-能量函数进行积分,得到第二段和第三段的纵程;对解析预测方法的精度和计算效率进行分析,结果表明该方法计算精度较高,速度快,可用于跳跃式再入轨迹的在线规划和制导。

Analytical downrange prediction of the first entry phase in skip entry for lunar module

For lunar module with low lift-to-drag ratio, Skip entry trajectory must be flown to extend downrange. The key element of skip entry trajectory online planning or predictive guidance is how to predict the downrange of the first entry phase rapidly and precisely. An Analytical method is proposed in this paper. First, closed-form approximate solution of the longitudinal equation of motion is obtained using matched asymptotic expansion method. Second, the first entry trajectory is divided into three phases. In the first phase, downrange is obtained using a repeated trapezoidal-rule integration. In the second and third phases, quadratic polynomial is used to fit the drag versus energy profile in each phase, and the polynomial coefficients are solved using the approximate solution, and downrange is obtained by integrating the reciprocal of drag versus energy profile. Third, the accuracy and computational efficiency of the proposed method is analyzed. Simulation results indicate that the method proposed in this paper has both high accuracy and computational efficiency, and is very suitable for online planning and guidance.