在地球极区无奇异的再入飞行器质心运动方程

传统的再入飞行器质心运动方程用经度和纬度描述地理位置，在南北极极点处奇异，在南北极区病态。本文提出利用位置矢量的三个方向余弦，称为“三余弦数”或“三元数”，代替经纬度，推导出无奇异再入质心运动方程。再入飞行器临近极点和到达极点的算例显示，使用三元数的无奇异再入方程完全避免了传统方程有关极点的奇异性。同时，无奇异方程所选状态变量与传统方程可进行很简便的转换。

Singularity Free Equations of Re-entry Vehicle Translational Motion in Polar Regions

The conventional translational equations of re-entry vehicle have singularities at the North and South Poles,and are ill-conditioned in the Polar Regions,for the geographic position is described by latitude and longitude.The direction cosines of the vehicle's position vector,called three-cosine or `trinion',are presented to replace latitude and longitude to derive the singularity free equations of re-entry translational motion.The singularity free equations were validated by two examples,in one of which the re-entry vehicle was close to the pole,in the other at the pole.The singularities of conventional equations in Polar Regions are completely avoided at the singularity free equations.The state variables of the new equations can be conveniently converted to those of the conventional equations.