航天飞机再入大气层最优轨迹

本文研究航天飞机再人大气层最小气动加热的最优轨迹。文中考虑了地球自转的影响和气动加热、动压、过载对再入飞行的限制。在地心非惯性坐标系中,采用球面速度坐标系建立运动方程。再入点的运动参数是在惯性计算系中给出的,故地心非惯性系的再入参数是经过惯性计算系到非惯性计算系的转换而获得的。文中最优轨迹的性能指标采用气动加热量的最小值,最优轨迹的求解方法采用非线性规划法,即将控制变量参数化,把泛函的极值问题转变成函数的极值问题进行求解,因而可以利用函数优化方法的标准程序进行计算。本文在性能指标中引进了罚函数,并采用Powell方法求解无约束的最优化问题。文中进一步用运动参数描述控制变量,这不但便于初值的选择,而且还便于考虑一些参数变化规律的要求。本方法使用方便,计算结果稳定可靠。

The Re-entry Optimal Trajectory of Space Shuttle

This paper investigates the re-entry optimal trajectory on the minimum aerodynamic heating of the space shuttle. The influence of Earth rotation and the constraints in aerodynamic heating,dynamic pressure and total load factor are considered. The motion c-quations are established with respect to rotating geocentric coordinate system. Since the motion parameters at the initial re-entry point are given in an inertial system,they must be transformed from the inertial system into a rotating system. The minimum aerodynamic heating is used as the performance index of optimal trajectory in this paper. The optimal trajectory is solved using nonlinear programming. The control variables are parameterized by means of an interpolating function,so the extremum problem of functional can be transferred into the extremum problem of the function. We use a standard function optimization program to solve the problem. By introducing a set of penalty functions,it is led to a problem of unconstrained optimization,which can be solved by Powell method. Then the control variable parameters are written as a function of motion parameters, so the initial value is easy to be selected. The method is convenient to use and the calculation results are stable and reliable.