共查询到18条相似文献,搜索用时 734 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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在电子计算机上自动推导Flora群小行星的普遍摄动I.Hansen方法应用 总被引:1,自引:0,他引:1
在IBKM 4341电子计算机上应用Hansen方法和运行Broucke R.开发的Poisson级数展开程序系统,自动推导了木星对Flora群小行星的普遍摄动,将将计算得到的摄动系数表与前人应用Bohlin群法所得相应表作了比对。由此得到结论:1.取代Bohlin群法,用在电子计算机上建立的Hansen方法程序能够既快又精确地计算小行星的普遍摄动;2.对于1000″<n<1100″(n为小行星的周日平均运动,单位以弧秒/日表示)情形,如果小行星轨道的偏心率e和交角i不太大,Stroemberg表是适用的,最大误差不到20″;3.对于n-1047″情形,因此时n′/n-2/7,接近通约状态(n′为木星的周日平均运动),必须计及(2-7)长周期项,而de la Villemarque所给出的公式不够精确;4.对于975″<n<1000″情形,Stromberg表因其精度低而不适用,当e,i较大时尤甚;5.对于n-997″情形,因此时n′/n-3/10,即接近另一种通约状态,必须计及(3-10)长周期项。 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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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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先进多孔径视宁度廓线仪(A-MASP)由两台小望远镜组成,通过望远镜观测太阳表面的米粒结构进行日间湍流廓线测量.两台望远镜之间的相对指向误差可以通过改进的湍流廓线测量公式消除.数值仿真研究表明,使用消除抖动的湍流廓线计算公式后,发现A-MASP对地表附近的湍流不敏感.当两台望远镜距离为0.4 m时,无法测量400 m以下的湍流.在A-MASP中,采样高度的不均匀分布会造成测量结果的失真,可通过等效采样高度的计算方法,对该失真进行修正.通过100层相位屏对大气湍流的仿真,结果表明当望远镜距离不同时,湍流廓线测量的结果各有侧重.当距离较近时(0.4 m),A-MASP对0.4–5 km的湍流廓线测量精度较高.当距离为1.2 m和2.0 m时,对5 km以上的湍流廓线测量较准确. 相似文献
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火星非球形引力位田谐项联合摄动分析解 总被引:2,自引:0,他引:2
火星非球形引力场模型与地球有明显差别,其非球形引力位中的田谐项系数基本都要比地球的相应值大一个量级,尤其是J2,2项(赤道椭率项)的大小接近它的动力学扁率项J2.对于低轨探测器,若要使轨道外推1 d弧段的精度达到500 m(相当于标准单位10-4量级),在构造环火探测器的轨道分析解时,田谐项与J2项以及田谐项与田谐项之间的联合摄动不容忽视.根据摄动量级分析和构造的摄动分析解证实,上述联合摄动对轨道沿迹方向的影响可超过10-4,并给出了数值验证.结果表明,与地球低轨卫星不同,在类似的问题中,构造环火卫星摄动分析解时,必须考虑这些联合摄动项的影响. 相似文献
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The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars’ tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J2. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10−4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10−4 in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration. 相似文献
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提出一种直接推导摄动运动方程的方法,也就是以矢量的微分运算为工具直接推导二体问题意义下的瞬时椭圆如何在摄动力三分力的作用下轨道根数发生的变化,推导过程几何图像清晰,力学意义明确.特别是对ω、M两根数的推导,比传统的方法更简洁、直观. 相似文献
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《Chinese Astronomy and Astrophysics》2022,46(1):137-151
Seven direct calculation methods of Hansen coefficients and their derivatives are reviewed. The computational efficiencies of these methods are compared, and their computational stabilities are analyzed. We show that the recursion relations of Hansen coefficients can be used to determine the stabilities of calculation results. Finally, it is pointed out that Wnuk's method (double precision computation) and McClain's methods (quadruple precision computation) are stable, which can be used to calculate orbit perturbations. Because of small orbital eccentricities of most satellites, the perturbation calculations without singularities are required, and McClain's first method (quadruple precision computation) is recommended. 相似文献
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J. Hagel 《Celestial Mechanics and Dynamical Astronomy》1992,53(3):267-292
A new analytic approach to the solution of the Sitnikov Problem is introduced. It is valid for bounded small amplitude solutions (z
max = 0.20) (in dimensionless variables) and eccentricities of the primary bodies in the interval (–0.4 < e < 0.4). First solutions are searched for the limiting case of very small amplitudes for which it is possible to linearize the problem. The solution for this linear equation with a time dependent periodic coefficient is written up to the third order in the primaries eccentricity. After that the lowest order nonlinear amplitude contribution (being of order z
3) is dealt with as perturbation to the linear solution. We first introduce a transformation which reduces the linear part to a harmonic oscillator type equation. Then two near integrals for the nonlinear problem are derived in action angle notation and an analytic expression for the solution z(t) is derived from them. The so found analytic solution is compared to results obtained from numeric integration of the exact equation of motion and is found to be in very good agreement.
CERN SL/AP 相似文献
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考虑地球扁率摄动影响的初轨计算方法 总被引:5,自引:0,他引:5
在二体问题意义下的短弧定轨,Laplace型方法是最主要最典型的一种初轨计算方法。若测角资料达到10^-4-10^-5精度(相当于2″—20″之间),那么要使定轨精度达到与其相应的程度,地球非球形引力位中的扁率项摄动应该考虑,在此前提下,同样可以采用相应的Laplace型定轨方法。即给出这种严格包含扁率摄动的初轨计算方法的原理和具体计算过程以及计算实例,除采用多资料定轨方法外,这种方法也是提高初轨计算精度的一种途径,它同样可用于多资料的情况,这种方法对于大扁率主天体(即中心天体)的卫星定轨将更有实用价值。 相似文献
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Tame Gonzalez Rolando Cardenas Israel Quiros Yoelsy Leyva 《Astrophysics and Space Science》2007,310(1-2):13-18
In this work we investigate the evolution of matter (linear) density perturbations for quintessence models with a self-interaction
potential that is a combination of exponentials. One of the models is based on the Einstein theory of gravity, while the other
is based on the Brans-Dicke scalar tensor theory. We constrained the parameter space of the models by using the determinations
of the growth rate of perturbations derived from data of the 2-degree Field Galaxy Redshift Survey.
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