轨道数值积分方法适用性研究

Analysis of Applicability of Orbit Numerical Integration Method

轨道积分是人造卫星轨道预报和精密测定中的重要环节,由于卫星受力情况复杂,精确的二阶运动微分方程的解析解难以求得,所以数值解法是解决轨道积分问题的主要手段。数值积分方法可分为单步法和多步法,每一类方法都有其特点和适用范围,在实际问题中如果选择不恰当的积分方法,精度或者计算速度将不能达到要求。以精度和计算效率为主要衡量指标,对Runge-Kutta法和Adams-Cowell法进行仿真,分别研究了两种方法的性能与轨道偏心率和轨道高度的关系,为卫星轨道积分方法的选择提供了依据。

The integration of orbit is an important part to satellite precise orbit determination and prediction. For the complex perturbations on the orbits, the accurate solution of its second order differential equations is impossible to obtain. Therefore, numerical integration is often used to evaluate its discrete solutions to satisfy certain accuracy. Numerical integration can be divide into two kinds： single-step method and multi-step method. Runge-kutta algo- rithm and Adams-Cowell algorithm are chosen as the typical representative to research performance of two meth- ods. The advantages and disadvantages of these algorithms are expounded by comprehensive analysis. The influences to accuracy and efficiency due to orbits＇ height and eccentricity are also studied to provide the basis for selecting optimal integration method.