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本文提出了弹道式飞行器自由飞行轨道的解析解法。首先,在一个特殊的非正交的绝对坐标系中建立了运动微分方程,其中考虑了具有一阶扁率系数的地球引力场模型,然后导出运动方程的解析解。其解的精度与所用地球引力场模型的精度是一致的。应用本文给出公式,只需给定发射惯性坐标系或地面发射坐标系中关机点或以后任一点参数,便可解析地求出其后任一点的轨道参数(飞行器在惯性空间中的位置矢量、速度矢量或相对于地球的位置矢量和速度矢量)。并附有若干计算结果,表明解析解法具有较高的精度。
In this paper, an analytical solution to the free-flight trajectory of ballistic aircraft is proposed. First, a differential equation of motion is established in a special non-orthogonal absolute coordinate system, in which the gravitational field model of the Earth with first-order flattening coefficient is considered and then the analytic solution of the equation of motion is derived. The accuracy of the solution is consistent with the accuracy of the Earth’s gravitational field model used. Applying this formula, the orbital parameters of any subsequent point (the position vector of the aircraft in inertial space, Velocity vector or position vector and velocity vector relative to the earth). And with a number of calculations, indicating that the analytical solution with high accuracy.