共查询到18条相似文献，搜索用时 109 毫秒
1.
综合评价线性多步积分公式轨道积分性能的两项新指标 总被引：1，自引：0，他引：1
徐继鸿 《中国科学院上海天文台年刊》2002,(23):34-39
概述了制约线性多步积分公式轨道积分状态的多种因素。提出了综合评价线性多步积分公式积分性能的两项新指标。建议在对数值计算有较高精度要求的科研项目中，应将构造并选择适合研究项目的线性多步积分公式以及高效的积分方式列为课题前期工作的重要部分。 相似文献
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推荐了一组对短、中、长积分间隔以及带耗散力或较大偏心率等多种类型卫星轨道数值积分皆可获取较高计算精度的线性多步积分公式（MTM）,供读者选择使用。 相似文献
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推荐数值求解y‘’=f（x,y）的几组织分系数 总被引：1，自引：1，他引：0
为求解特殊二阶常微分方程ｙ＇＇＝ｆ（ｘ，ｙ）的初值问题，本文采用最大阶算子方法构造了一类线性多步积分公式，并与Ｃｏｗｅｌｌ方法的同阶公式作了大量的平等计算，通过对不同轨道类型、不同步长、不同积分间隔时的计算结果的全面仔细地分析比较，我们从八阶、十阶、十二阶、十四阶中各自选定一组积分系数，推荐给同行计算使用，结果表明，采用本文推荐的积分方法计算天体轨道是有益的，因为它的积分精度以及积分过程中误差累积 相似文献
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为求解特殊二阶常微分方程ｙ″＝（ｘ，ｙ）的初值问题，本文采用最大阶算子方法构造了一类线性多步积分公式，并与Ｃｏｗｅｌｌ方法的同阶公式作了大量的平行计算，通过对不同轨道类型、不同步长、不同积分间隔时的计算结果的全面仔细地分析比较，我们从八阶、十阶、十二阶、十四阶中各自选定一组积分系数，推荐给同行计算使用，结果表明，采用本文推荐的积分方法计算天体轨道是有益的，因为它的积分精度以及积分过程中误差累积的方式都十分明显地好于同阶的Ｃｏｗｅｌｌ方法。 相似文献
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适用于人造卫星轨道数值积分的线性多步法的研究 总被引：4，自引：0，他引：4
总结了多年来构造适合卫星轨道计算的线性多步积分方法的研究进展;介绍了在构造积分公式的过程中选取伪根的三条原则。结合具体算例,对推荐的适用于不同类型卫星轨道的五线性多积分公式的性能与对称文坛及科威尔方法作了详细地比对和评述。 相似文献
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保持Runge-Lenz向量的数值方法 总被引：2，自引：2，他引：0
对孤立积分和能够保持Runge-Lenz向量的梯形公式进行详尽讨论．孤立积分就是限制粒子运动区域的不变量，具有n个自由度的自治可积哈密顿系统且只有n个互相对合的独立孤立积分，并且其他孤立积分的存在对粒子的运动是有意义的，Kepler二体系统存在能量积分、角动量积分和Runge-Lenz向量．对于平面运动情况，这三类积分中只有3个独立孤立积分；而对于三维空间情形，该三类积分仅有5个是独立的．就前者而言，Kepler二体平面运动积分构成该系统中的对称群SO（3），经过Levi-Civita变换，它可以转化为二维各向同性谐振子系统中的对称群，而该对称群能够被梯形公式准确保持，另一方面，对于后者梯形公式对这三类积分的严格保持还可以在5个Kepler轨道根数n、e、i、Ω和w上得到体现。 相似文献
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可用于带耗散力卫星轨道长间隔积分的数值积分方法 总被引：2，自引：0，他引：2
本文分析了对称方法不适合带耗散力的卫星轨道长间隔积分的缺陷和本质原因,并针对这个问题,采用文所介绍的方法,构造并推荐了一组积分公式。 相似文献
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Adams—Cowell方法与KSG积分器的比较 总被引：2，自引：0，他引：2
在人造地球卫星精密定轨中,有摄星历等量的计算常采用Adams-Cowell方法,美国Texas大学空间研究中心(CSR)的定轨软件中则采用了一种有别于Adams-Cowell方法的KSG积分器。本文对这两种线性多步法作了全面比较,并用典型算例作了数值验证,列出了两种方法中卫星轨道沿迹误差的状况,以此表明为什么人们常采用Adams-Cowell方法。 相似文献
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Numerical integration methods for orbital motion 总被引：1，自引：0，他引：1
O. Montenbruck 《Celestial Mechanics and Dynamical Astronomy》1992,53(1):59-69
The present report compares Runge-Kutta, multistep and extrapolation methods for the numerical integration of ordinary differential equations and assesses their usefulness for orbit computations of solar system bodies or artificial satellites. The scope of earlier studies is extended by including various methods that have been developed only recently. Several performance tests reveal that modern single- and multistep methods can be similarly efficient over a wide range of eccentricities. Multistep methods are still preferable, however, for ephemeris predictions with a large number of dense output points. 相似文献
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In this paper, a new family of explicit and implicit multistep methods is presented both for the error-controlled and uncontrolled modes. The main concept is to replace the Newton interpolation with the Hermite interpolation, where the Hermite polynomial is fitted to the function values and its derivatives. This idea is very useful in the numerical solution of problems (e.g., orbit propagation problem) where higher-order derivatives can easily be computed. In addition to the theoretical concept, the stability regions of the proposed methods are determined. The new methods are more stable than the well-known multistep numerical integrators (i.e., Adams–Bashforth and Adams–Bashforth–Moulton) in the explicit, implicit, and predictor–corrector forms. Using the second-order derivatives gives smaller error constants in the proposed method. The new integrators are numerically tested for a few examples, and the solutions are compared with those of the well-known multistep methods. Moreover, the CPU time and absolute integration error are compared in the satellite orbit propagation problem using various integration methods. The CHAMP mission, i.e., a German small-satellite mission for geoscientific and atmospheric research and applications, is considered as a case study for comparing the achievable accuracy of the proposed method with the existing method for solving the two-body problem. 相似文献
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P. Moore 《Celestial Mechanics and Dynamical Astronomy》1978,17(3):281-297
Lambert and Watson (1976) examine the family of symmetric linear multistep methods for the special second-order initial value problem, and connect the property of symmetry with a property of periodicity. The problems of celestial mechanics may be formulated as second-order initial value problems, but these frequently incorporate the first derivative explicity. It is common for such equations to be reduced to a system of first-order equations. Thus motivated, we utilize ideas from the aforementioned paper to determine the family of linear multistep methods for first-order initial value problems that possess an analogous property of periodicity. This family of orbitally stable methods is illustrated by examining the regularized equations of motion of an artificial earth satellite in an oblate atmosphere. 相似文献
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A preliminary survey of multiderivative multistep integrators is carried out. It is found that all of them are much more accurate than the classical linear multistep methods, but most of them have poor stability. After parameter adjustment, two of them (called MDMS I and MDMS II by us) are competitive with or superior to the classical methods in some aspects, such as accuracy and stability. MDMS I behaves especially well in all the cases which have been studied. 相似文献
16.
Hamilton系统数值计算的新方法 总被引：7，自引：0，他引：7
系统地介绍了近年来对Ｈａｍｉｌｔｏｎ系统数值计算新建立的辛算法和线性对称多步法，并对它们在动力天文中的应用作了一简要回顾。 相似文献
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A new class of linear multistep methods is proposed for the solution of the equations of motion of certain dynamical systems encountered in celestial mechanics and astrodynamics. These methods are distinguished from the classical predictor-corrector methods in that they permit back-corrections of the solution to be made. As the integration advances in time, the numerical solution is corrected or improved at certain points in the past. The enhanced numerical stability of these methods allows the meaningful application of high-order algorithms. Consequently, stepsizes larger than those attainable with the classical methods may be adopted and thus greater over-all efficiency may be realized. The application of these methods to the problem of determining the orbit of an artificial satellite is accomplished and the results are compared with those obtained using classical methods. 相似文献
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Ben K. Bradley Brandon A. Jones Gregory Beylkin Kristian Sandberg Penina Axelrad 《Celestial Mechanics and Dynamical Astronomy》2014,119(2):143-168
We describe a new method for numerical integration, dubbed bandlimited collocation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer force function evaluations than explicit Runge–Kutta schemes. In particular, we use a low-fidelity force model for most of the iterations, thus minimizing the number of high-fidelity force model evaluations. We also investigate the dense output capability of the new scheme, quantifying its accuracy for Earth orbits. We demonstrate that this numerical integration technique is faster than explicit methods of Dormand and Prince 5(4) and 8(7), Runge–Kutta–Fehlberg 7(8), and approaches the efficiency of the 8th-order Gauss–Jackson multistep method. We anticipate a significant acceleration of the scheme in a multiprocessor environment. 相似文献