基于轨道要素差的纬度辐角差表达式

Latitude argument difference expression based on orbit element difference

为避免在求解不同相对距离下的相对轨道时,用相对坐标会遇到1组相互耦合的非线性微分方程的情况,采用轨道要素差法解决该问题.首先定义轨道要素差矢量并通过引入1个描述卫星角位置的分量对其进行改写;然后建立相对轨道的轨道要素差表达式和纬度辐角差表达式,明确纬度辐角差是描述相对轨道时唯一需要的变量;最后得出不同相对距离条件下相对轨道的纬度辐角差表达式并说明区别远、近距离条件下相对轨道的必要性.根据推导的基于轨道要素差的相对轨道表达式进行仿真,结果表明用基于纬度辐角差表达式来求解相对轨道是正确的.

To avoid a set of coupled nonlinear differential equations while solving the relative orbit under different relative distance, a method of orbit element difference is used to solve the problem. Firstly, an orbit element difference vector is defined and rewritten by introducing a component which describes the satellite angular position. Secondly, the expressions of relative orbit difference and latitude argument difference are established to make sure that the latitude argument difference is only the desired variable to illuminate a relative orbit. Finally, the latitude argument difference expressions of relative orbits are obtained under different relative distance conditions, and the necessity of distinguishing the relative orbits under the different distance conditions is explained. The simulation is done according to the deduced relative orbit expressions which are based on orbit element difference, and shows that it is correct to use the expressions based on the latitude angle difference to solve the relative orbit.