【作者】 刘承志；

【导师】 崔斗星；

【作者基本信息】 中国科学院研究生院（上海天文台） ， 天体测量与天体力学， 2002， 博士

【摘要】 描述人造卫星运动的微分方程非常复杂，不可能给出解的解析表达式。由天体摄动运动方程给出的小参数幂级数解等分析解满足不了人造卫星应用所需要的定轨精度要求，这就使得解常微分方程的数值方法在卫星动力学方法中占有十分重要的地位。　　本文从应用的角度研究了天体运动方程的数值解法。首先，目前在卫星动力学中常用的所有人造卫星运动方程的数值解法有待改进的最重要的问题就是稳定性问题。无论是单步法还是多步法，某一步产生的误差都会传播下去，误差将会积累。当这种误差的积累得到控制时，对应的数值解法才是稳定的。　　数值稳定性问题与步长的选择有关。定步长的缺点在于不管是积分曲线的各个点的曲率如何都取一样的步长，这样肯定会在曲率大的一些点带来比较严重的误差，这种误差将在每一步的计算中积累。如果以积分曲线每一步的曲率大小来控制步长大小，可以避免这种累积误差。从这个想法出发，在文中实现了以积分曲线的曲率控制步长大小的作法，在曲率大的点步长小，而在曲率小的点步长大，这是非常合理的选择，也是本文的一个创新点。　　其次，众所周知Taylor级数法虽然公式简单且数值稳定性好，但是高阶导数的计算非常麻烦，难以实用。在本论文中，给出了以右函数f 在一些任意点的值表示x 在 点的高阶导数的方法，从而把人造卫星运动方程的数值解法转化为非线性方程组的迭代求解法。这种积分器精度高，数值稳定性也好。<WP=7>　　本文作者同时作了激光测距技术在人造卫星精密定轨中的应用方面的一些研究工作，利用全球激光测距资料对Lageos-1卫星进行了定轨，精度达到1cm，并归算了长春SLR站的站坐标。分析了长春站的观测资料的处理结果，得出一些结论。进而设计了长春SLR站实现白天观测的实施方案。更多还原

【Abstract】 The differential equations that describe the artificial satellite motion are very complicated, and it is impossible to get the analytic express of solution. Its analytic solution such as small parameter power series solution cannot meet the orbit determination accuracy that artificial satellite application needs. So this makes numerical method in ordinary differential equations for the satellite dynamics occupy very important position.This paper studied the numerical methods in celestial motion equations from the applied aspect. First, now in all common numerical methods for the satellite dynamics equations the most important problem that needs to be improved is stability problem. Whether are a single-step methods or multi-step methods, the error in calculating every step will spread and accumulate. When the error accumulation can be controlled, the relative<WP=9>method is just stable.Numerical stability is relative with the choice of step-size. The weakness of fixed step-size is that step-size is not variable regardless the curvature of each point of the integral curve change or not, which will affirmatively bring serious error in these points that the value of curvature is bigger. And, this kind of error will accumulate in calculating process. If the change of step-size is controlled by the value of curvature of integral curve, the result can avoid such an error accumulation. From this viewpoint, we fulfilled to control the step-size with the curvature of integral curve. The step-size is smaller in calculating these points that the value of the curvature is bigger and the step-size is bigger in calculating these points that the value of the curvature is smaller, which is rather reasonable choice and is also a creative point in this paper.The next in order, it is well known that the formula of Taylor series method is simple and its stability is good, but its high level derivative is not easy to be gotten and so it is difficult in practice. This paper points out that the values of the right function at arbitrarily points can express the high level derivatives of at , and gives out the formulas. So we translated the numerical methods for artificial satellite motion equation into the iterative method for a set of nonlinear equations. This kind of integrator is high accurate and great stable.Author also did some research work for the application of Satellite Laser　Ranging(SLR) technique to precise orbit determination. We calculated the<WP=10>orbit elements of Lageos-1 with using the worldwide SLR data and the orbit accuracy attain 1 cm, meanwhile calculated the coordinates of Changchun SLR Station. Some conclusions were gotten by analyzing the data processing results of Changchun SLR Station. Further more, author designed an implementary project for daytime observation at Changchun SLR Station.更多还原