半分析方法及其在地球卫星轨道长期演化中的性能评估

发布时间：2018-01-01 08:30

本文关键词：半分析方法及其在地球卫星轨道长期演化中的性能评估　出处：《南京大学》2016年硕士论文　论文类型：学位论文

【摘要】：这篇论文根据作者在硕士生期间参加的一项课题撰写而成,旨在研究半分析方法运用于地球卫星轨道长期预报的性能(速度和精度),并给出半分析法针对不同类型轨道可供参考的精度和速度。第一章绪论部分。首先,介绍了本课题的背景,即为了能够充分掌握空间目标的长期演化规律和分布情况,需要对它们的轨道进行长期预报,考虑到速度和精度的实际需求,半分析方法是一种十分合适的预报手段。虽然半分析法不是一种新方法,但是几乎找不到定量评估其性能的文献,这给一些实际应用造成了困难。在这样的前提下,我们定量分析了半分析法在常用地球卫星轨道中的精度和速度,该结果可以帮助我们了解半分析法在长期预报中的适用性。其次,介绍了半分析方法目前国内外的研究情况。最后,简单介绍了论文中用到的时间系统、坐标系统、摄动方程和单位系统。第二章介绍现有卫星预报方法。众所周知,卫星轨道预报实为求解一个常微初值问题的方程组,目前较为流行的有三种做法,即数值法、分析法和半分析法。数值法,即利用数值积分器一步步外推初始根数,直到到达预报时间点。该方法的优点是实现简单,精度高,缺点则是计算耗时较长。分析法,即显式地给出各个根数在受摄二体问题下的分析解,由于已经给出了摄动解,所以在有了初始根数的情况下,可以方便地直接给出预报时间点处的根数。它的优点是速度快,因为不用像数值法一样一步一步外推,缺点则是受到收敛弧段的限制预报时间不宜过长,一般情况下为103弧段(归一化单位下)。半分析法利用数值方法积分平均化后的动力系统。求解则采用数值法外推,因此可以想象其精度优于分析法而速度将优于数值法。半分析法的核心内容就是如何得到平均化右函数,因此着重介绍了分析平均和数值平均两种平均化方法,并简单比较了两者的性能,阐述了最终选择分析平均的理由。第三章各摄动力在半分析法中的处理。本章依次介绍非球形、第三体、光压、大气在半分析法中的具体处理细节。每新增一个摄动源的同时,将半分析法应用于不同高度卫星,以便直观地了解新的摄动源带来的动力学特征以及对于精度和速度的影响。第四章将半分析方法运用于不同类型轨道。首先,通过简单的算例给出半分析法不同轨道高度适合的非球形引力阶次。而后,将完整力模型的半分析方法运用于不同类型地球卫星轨道,研究在不同初始根数a,i的组合下,半分析法在100年尺度长期预报中的精度。地球卫星轨道按高度主要划分为低轨(有大气),低轨(无大气),12小时中轨及24小时高轨地球同步。通过比较大量的算例后发现,相比于数值法,半分析法100年尺度下瞬时根数a,e,i的精度误差在O(10-3)量级,Ω的精度误差在10°之内。虽然右函数精确到二阶的半分析法在大部分情况下都表现出了良好的性能,但是仍然会遇到一些特殊算例,半分析法的表现不尽如人意。这些算例有些伴随着特殊的动力学现象,有些则归咎于处理方法上的原因。前者,我们在本章中就给出了解释；后者,我们将在第五章中提出合理的解决方案。第五章特殊问题讨论。首先解释了第四章中倾角i=90°时半分析精度下降问题,而后给出了大偏心率轨道的处理方法,接着讨论了坐标系附加摄动中的补充项在半分析法中是否有必要添加,最后讨论了低轨根数误差图中的“岛状”结构成因。文章针对不同类型的地球卫星轨道,定量地展示了半分析法100年尺度长期预报的性能。当然这里只是一些基础性的精度和速度的讨论,半分析法的应用范围远不止如此,比如卫星碰撞后碎片分布的快速估计,空间目标编目中的定轨、关联等。希望本文的工作可以给相关领域的工作者起到一定借鉴意义。
[Abstract]:This paper according to the author in the master a subject in writing during a performance to study the semi analysis applied to long-term earth satellite orbit prediction (speed and accuracy), and gives a semi analytic method for different types of track reference accuracy and speed. The first chapter is the introduction part. First, introduced. The background of this project, the long-term evolution and distribution in order to be able to fully grasp the space target, they need to track the long-term forecast, considering the actual demand of speed and accuracy, the semi analytical method is a suitable forecasting means ten. Although the semi analytic method is a new method, but rarely found to evaluate quantitatively the performance of literature, which caused difficulties for some practical applications. In this context, we quantitatively analyzed the semi analysis method commonly used in the earth satellite orbit in precision and speed, The applicability of the results can help us understand the semi analytical method in the long-term forecast. Secondly, the semi analytical method of research at home and abroad. Finally, briefly introduces the time system of paper used in the coordinate system, perturbation equation and unit system. The second chapter introduces the existing satellite prediction method. As everyone knows, equation group is a satellite orbit prediction solving ordinary differential initial problems, the more popular there are three approaches, namely numerical method, analytical method and semi analytical method. The numerical method, namely the use of numerical integrator step by step extrapolation of initial root number, until the arrival of the forecast time. This method is simple, high precision the disadvantage is that, long calculation time. Analysis is given to show the number of each root analysis in the perturbed two body problem solution, as has been given a perturbation solution, so in the initial number of roots under the condition that the party can Give forecast time point. It is the root number advantage is speed, not because of the same step by step extrapolation like numerical method, the disadvantage is that by the convergence of arc limit prediction time should not be too long, generally 103 arcs (normalized units). By using the method of dynamic system analysis the numerical method of integral average. After is solved by numerical method of extrapolation, so you can imagine its precision analysis and speed will be better than the numerical method. The core content of semi analytic method is how to get the average of the right function, so the article introduces two kinds of numerical analysis and the average average average method, and compares the two the performance, describes the final choice analysis of average reason. In the third chapter, the perturbation analysis method in processing power in half. This chapter introduces the non spherical, third body, light pressure, atmospheric specific in the semi analysis method in detail. Every new perturbation source at the same time, the application of semi analysis method in different altitude satellite, in order to intuitively understand the dynamic characteristics of moving source perturbation brings and the influence on the precision and speed. The fourth chapter will analysis methods used in different types of rail. First of all, through simple numerical example gives the semi analytic method different orbit height for non spherical gravitation order. Then, the semi analytical method of complete stress model used in different types of satellite orbit, research in different initial root number a, the combination of I, the accuracy of semi analytical method in the long-term 100 year scale forecast. The earth satellite orbit is mainly divided into the low in height rail (air), Leo (without air), 12 hours and 24 hours in orbit for high orbit geostationary. By comparing a large number of examples that, compared to the numerical method, the semi analytical method of instantaneous root 100 years scale number a, e, I of the precision of the error in O (10-3) The magnitude of error, Omega in 10 deg.. Although the semi analytical method for two order accurate to the right function in most cases showed a good performance, but will still encounter some special examples, semi analytic method is unsatisfactory. It is accompanied by some special reasons some dynamical phenomena. Is responsible for processing methods. The former, in this chapter we give the explanation; the latter, we will put forward reasonable solutions in the fifth chapter. The fifth chapter discusses the special problems. The fourth chapter firstly explains the inclination of i=90 degrees and semi analytical accuracy, then the processing method of large eccentricity the track, then discussed the coordinate additional perturbations in the supplementary terms in the semi analysis whether it is necessary to add, finally discussed the low orbit error root number chart in the "island" structure. The reasons for different types. The ball satellite orbit, quantitatively demonstrate the performance of semi analytical method for 100 years scale long-term forecast. Of course there are only some of the accuracy and speed of the discussion, the scope of application of semi analytical method is far more than that, such as rapid estimation of debris distribution satellite collision, orbit, space object catalogue in relation to. Reference is hoped that this work can give workers in the field.

【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P173

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