共查询到19条相似文献,搜索用时 343 毫秒
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在推导倾角函数的递推公式时,通常利用(A)1Al-1,m,p(I)+A2Al,m,p(I)+A3Al+1,m,p(I)=0和(C)1Al,m,p-1(I) +(C)2Al,m,p(I)+(C)3Al,m,p+1(I)=0来定义倾角函数的l递推和p递推.指出:这样建立的递推公式将包含cosI=1/n(n为整数)的奇点,使得倾角函数的计算出现错误.该奇点可以通过改变l递推和p递推的定义来克服. 相似文献
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推导了超几何级数两种重要的递推关系,并利用这些关系,推导出Gooding的倾角函数递推公式.此外,证明基于Jacobi多项式的递推关系,也可导出该递推公式,并且推导过程比超几何级数的递推更加简单.揭示了Gooding方法的实质是Jacobi多项式的递推. 相似文献
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利用d-函数的Blanco递推(d-funl)和Risbo递推(d-fun2),可以得到两种计算倾角函数及其导数的方法.这两种方法均有较高的精度和稳定性.对于小倾角,d-fun2的精度优于d-fun1,而对于大多数其他倾角,d-fun1的精度优于d-fun2;但d-fun2的稳定性明显优于d-funl;计算速度d-funl比d-fun2约快7倍.但是这两种方法均有sin I=0的奇点.另外,d-函数方法直接计算出来的就是正规化的倾角函数,不能实现倾角函数的无奇点计算,因此不适合在小倾角卫星动力学中应用. 相似文献
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历史上曾经提出了较多的倾角函数递推算法,但有一些已经被证明在高阶是不稳定的.通过对递推方向上倾角函数的数量级分析,可以判断倾角函数递推的稳定性.对于常用的3项递推,只有Mk(l)递推是稳定的,其他递推均是不稳定的.但是对于多项递推比较复杂,还需深入分析. 相似文献
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倾角函数是天体力学分析理论中一种常用的函数.当把摄动方程展开成时间和根数的形式时需要用到.历史上提出了很多经典的倾角函数递推算法,并在双精度平台下开发了Fortran程序.进行了1次四精度计算倾角函数的试验,结果表明:L平面递推方法的四精度计算精度可达10-22,计算速度比双精度Jacobi方法快6倍. 相似文献
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田谐项摄动是分析法轨道预报中的重要部分,其中包含大量倾角函数及其偏导数的计算.由于具有精度更高、速度更快的优点,倾角函数一般通过递推方法计算.以文献中提出的改进Gooding方法为基础,将其给出的程序稍加改进,在计算2–50阶倾角函数时缩短了约24%的计算时间.考虑到分析法预报过程中轨道平倾角变化很小,以泰勒展开式计算倾角函数,可极大提高计算速度,较大程度地减小分析法预报耗时,且引力场阶次越高,减小幅度越大,取50阶时预报耗时缩短了48%.另一方面,以2阶展开式计算倾角函数时,与改进Gooding法相比,分析法预报星历偏差很小.对于500 km高度的低轨卫星,分别以改进Gooding法和2阶泰勒展开式计算倾角函数,预报3天,当地球引力场阶次不高于50时,二者预报星历偏差RMS (Root Mean Square)低于1 mm,且随着轨道高度的增加,预报星历偏差RMS逐渐减小. 相似文献
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《Chinese Astronomy and Astrophysics》2013,37(3):315-327
In this paper, a method to calculate the inclination function with Jacobi polynomials is studied, the formulation of this method is very simple, it needs not to concern about whether k and l have the same parity, and to calcu- late the non-integral factorials, nor to concern about the conversion between the case of k < 0 and the case of k ≥ 0, and the recurrent formula can be the stan- dard recurrent formula for Jacobi polynomials. In addition, its computational accuracy and applicable order-numbers are equivalent to those of the Gooding method, but its calculating time is shorter than that of the Gooding method for 9%. 相似文献
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邓幼俊 《紫金山天文台台刊》1999,18(4):375-379
本文用非线性规划方法探讨了初轨确定问题。测角观测误差看作为参数的微摄动,而非线性规划的灵敏性分析模型(fhp) 建立在无摄动的情况下。由此,得出了在一阶近似下轨道根数计算值和测角观测误差值间关系的分析表达式。 相似文献
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严豪健 《中国科学院上海天文台年刊》2004,(1)
回顾了作为实用天文学和大地测量学中基本研究课题之一的大气折射映射函数研究的进展。介绍了近几年上海天文台发展的大气折射母函数方法 ,以及由此导出的大气折射解析解。对如今广泛地应用在空间测量技术中的几种映射函数做出评述 ;分析了NMF模型的优点和不足之处。介绍了由大气折射母函数方法引出的大气延迟新连分式映射函数和天文大气折射的映射函数方法。利用VLBI实验中高度截止角与基线长度重复率的关系、探空气球 (radiosonde)观测资料、PRARE资料比较了各种映射函数的结果。特别指出了映射函数方法对天文大气折射和光学波段测距精度的改进。讨论了大气折射计算中的主要误差源。 相似文献
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用非线性规划方法处理初轨计算问题,将观测误差看成参量的微小扰动量。在无摄情况下,建立了非线性规划中的灵敏度分析模型(fhp)。由此推导,在无摄情况下关于角资料观测误差对角资料观测真值的影响的误差传播分析公式(一阶近似)。 相似文献
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Two kinds of recursion relations of hypergeometric series were derived, and hereby the Gooding's recursion formula of inclination function. In addition, it was demonstrated that this recursion formula can be derived also on the basis of the recursion relation of Jacobi polynomials. Comparing with the hypergeometric series, the recursion process based on the Jacobi polynomials is much simpler, indicating that the Gooding's method is the recursion of Jacobi polynomials in essence. 相似文献
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给出了一种倾角函数及其导数的定积分计算方法,表达式十分简单,其计算精度:倾角函数可达10-15,导数可达10-13,可与Gooding方法相媲美.该方法的稳定性和适用倾角范围均较好,可供倾角函数的最高阶数Lmax≤50时使用. 相似文献
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本文根据误差理论,对PUVM2测轨方法的误差及其传播规律进行了初步的分析和研究,给出了卫星的轨道根数σ和空间位置r↑→的内符合误差估计公式。 相似文献
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On the inclination functions and a rapid stable procedure for their evaluation together with derivatives 总被引:2,自引:1,他引:1
The authors’ individual work on the inclination functions over a period of more than 30 years has led to the need for a joint
paper. Intervening papers by other authors have demonstrated misunderstandings needing to be corrected, in particular concerning
the key recurrence relation published by the present first author in 1971. This relation is remarkably stable, though this
has not always been recognized. The real source of error with the specific functions that are involved in the recurrence relation
arises from the possibilities for underflow (as well as overflow) in the computation. The problem exists even with normalized
versions of the functions, and is carefully addressed. Very important, for both academic and practical reasons, is a general
invariance relation that had been found earlier by the second author, for which a proof is given here for the first time.
Some numerical results from our new (and highly efficient) procedure for computing the inclination functions are tabulated,
and comparisons made with the results of other authors. Finally, Fortran code for an optimized implementation of this procedure
is in supplementary material.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
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Different formulas for computation of the inclination function in terms of nonsingular elements have been presented and compared. Among the ways to compute the inclination function presented below, the best one is based on the recurrence relations (eqs. 16) derived in this paper. 相似文献