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为了评价终段交会机动的各种不同方法,需要知道一个飞行器相对于另一个飞行器的自由飞行运动。当一种参考坐标系选在目标飞行器上时,这时要解的运动方程为一组系数为时间的显函数的变系数非线性微分方程组。本文给出了用扰动法解方程组得到的近似解析解。对于目标轨道偏心率较小和相对距离较大的情况下,这种解比过去找到的解更具有一般性。因此它广泛地用于研究近地轨道的问题。数值例举用来评价其解的精确度。结果表明,在一定的相对距离内现有的包含非线性的解必须代替以前基于线性理论的解。本文的解含有某些非线性效应。本文也给出了在预定时间内达到交会所必需的速度分量的近似解析解。
In order to evaluate the different methods of final rendezvous, it is necessary to know the free-flight movement of one aircraft relative to the other. When a reference coordinate system is selected on the target aircraft, the equations of motion to be solved at this time are a set of nonlinear differential equations with variable coefficients of time function. In this paper, the approximate analytic solution obtained by perturbation method is obtained. In the case of small eccentricity and relative distance of the target orbit, this solution is more general than the solutions found in the past. It is therefore widely used to study the issue of near-Earth orbit. Numerical examples are used to evaluate the accuracy of the solution. The results show that existing solutions containing nonlinearities must replace the previous linear theory-based solutions over a relative distance. The solution to this paper contains some nonlinear effects. This paper also gives an approximate analytical solution of the velocity components necessary to achieve the rendezvous within a predetermined time.