共查询到20条相似文献，搜索用时 46 毫秒
1.
S. J. Aarseth 《Astrophysics and Space Science》1971,14(1):118-132
A fourth-order polynomial method for the integration ofN-body systems is described in detail together with the computational algorithm. Most particles are treated efficiently by an individual time-step scheme but the calculation of close encounters and persistent binary orbits is rather time-consuming and is best performed by special techniques. A discussion is given of the Kustaanheimo-Stiefel regularization procedure which is used to integrate dominant two-body encounters as well as close binaries. Suitable decision-making parameters are introduced and a simple method is developed for regularizing an arbitrary number of simultaneous two-body encounters. 相似文献
2.
In this paper, we consider a statistical method for distance determination of stellar groups. The method depends on the assumption
that the members of the group scatter around a mean absolute magnitude in Gaussian distribution. The mean apparent magnitude
of the members is then expressed by frequency function, so as to correct for observational incompleteness at the faint end.
The problem reduces to the solution of a highly transcendental equation for a given magnitude parameter α. For the computational developments of the problem, continued fraction by the Top-Down algorithm was developed and applied
for the evaluation of the error function erf(z). The distance equation Λ(y) = 0 was solved by an iterative method of second order of convergence using homotopy continuation technique. This technique
does not need any prior knowledge of the initial guess, a property which avoids the critical situations between divergent
and very slow convergent solutions, that may exist in the applications of other iterative methods depending on initial guess. 相似文献
3.
Mohamed Adel Sharaf Mervat El-Sayed Awad Mona A. Banaja 《Astrophysics and Space Science》1987,133(2):339-353
In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for the KS regularized theory will be established for any numberN of the zonal harmonic coefficient. A general recursive computational algorithm based on these formulae is also established for the initial value problem of the KS theory for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding toN=2 andN=36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm. 相似文献
4.
In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulae is also established for the initial value problem of Burdet oscillator for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36.A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.Dept. of Astronomy, KAU 相似文献
5.
I. L. Andronov 《Astronomische Nachrichten》1994,315(5):353-370
Analytical expressions were derived for the expectation of the autocorrelation function (ACF) corresponding to lowfrequency least squares fits and deviations from them in the case of a limited number of observations N. A vector of values of the autocovariation function may be obtained by multiplication of a N . N matrix Z (dependent on concrete basic functions used for trend determination) by a vector of the unbiased ACF. Because much computational time is needed to obtain such a matrix, its components are to be computed once for concrete N and basic functions, and then stored as a file. An algorithm is proposed for determining the contribution of the correlated signal to the ‘signal+noise’. The expressions are written for general form of the ACF, and illustrated by the application to autoregressive models. The statistical properties of the model parameters are studied. The method is applied to cataclysmic binaries AM Her and TT Ari. The precise expressions allow us to obtain reliable results and to avoid misinterpretation being possible when using the approximate methods. 相似文献
6.
Sandro da Silva Fernandes 《Celestial Mechanics and Dynamical Astronomy》2003,87(3):307-315
In this paper the new approach for the integration theory of the canonical version of Hori method recently proposed is extended to the non-canonical one. It will be shown that the non-homogeneous ordinary differential equation with an auxiliary parameter t* associated with the mth order equation of the algorithm can also be replaced by a non-homogeneous partial differential equation in the time t. Using a generalized canonical approach, the general algorithm proposed by Sessin is then revised; as well as the Lagrange variational equations for the non-canonical version of Hori method. A simplified algorithm derived from Sessin's algorithm is presented for non-linear oscillations problem. 相似文献
7.
We present a new numerical method for solving the system of partial differential equations describing the structure and evolution of a spherically symmetric star. As usual, we employ the transversal method of lines in order to split the equations into a coupled spatial and temporal part. The novel features of the algorithm are the following: (a) Instead of using the Lagrangian picture we formulate the system of partial differential equations in the Eulerian picture. (b) We reformulate the equations of stellar structure as a multipoint boundary-value problem. By means of this reformulation the rather clumsy iterative matching procedure of stellar atmosphere and interior is avoided. (c) The multipoint boundary-value problem is solved by the multiple shooting method. This approach not only ensures a high accuracy of the stellar models calculated at each time step but also allows the free boundaries inside the star due to different energy transport mechanisms to be located exactly. (d) The time derivatives involved in the stellar-structure equations are discretized implicitly to second order accuracy. Moreover, at each time step, the chemical abundances are determined by using a sophisticated update procedure. In this way, a high accuracy is achieved with respect to the integration in time. The algorithm has turned out to be exceedingly reliable and numerically accurate. This is shown by the evolution of a 1 M⊙ star up to the hydrogen-shell burning phase. In this example, the virial theorem, the law of mass conservation, and the law of energy conservation is fulfilled to a hitherto unattainable degree of accuracy. Since the multiple shooting method, which is at the heart of our approach, is a perfect example of a parallel algorithm, the computational speed of the algorithm might be substantially improved provided easy-to-program, high-performance parallel computers with sufficiently many processors become available in the near future. 相似文献
8.
In this paper, general model analysis of the form c
i
i
() for the fractional loss of lightf() exhibited by a close binary system will be considered in the sense of the least-squares criterion. A general recursive method will be established for constructing the normal equations for the most useful functions
i
(), and an economical storage of the method on a digital computer, with its computational steps, will also be given. Moreover, a full recursive computational algorithm for the least-squares approximation will also be established. By means of this algorithm, all the solution vectors, the variance for different orders of fit and the corresponding variance-covariance matrix could be computed once and for all and, moreover, recursively. The economical storage of the algorithm and its computational steps will be given. Finally, some of the practical difficulties encountered in the application of the least-squares criterion will be analysed, and some techniques for detecting and controlling these difficulties are also given. Numerical examples on the Algol system using a Fourier cosine series of the form c
i
cos [(j - 1)
/] will be given for illustration. 相似文献
9.
Mohammed Adel Sharaf Mervat El-Sayed Awad Samiha Al-Sayed Abdullah Najmuldeen 《Earth, Moon, and Planets》1991,55(1):21-44
In this paper, the connections between orbit dynamics and rigid body dynamics are established throughout the Eulerian redundant parameters, the perturbation equations for any conic motion of artificial satellites are derived in terms of these parameters. A general recursive and stable computational algorithm is also established for the initial-value problem of the Eulerian parameters for satellites prediction in the Earth's gravitational field with axial symmetry. Applications of the algorithm are considered for the two cases of short and long term predictions. For the short-term prediction, we consider the problem of the final state prediction of some typical ballistic missiles in the geopotential model with zonal harmonic terms up to J
36, while for the long-term prediction, we consider the perturbed J
2
motion of Explorer 28 over 100 revolutions. 相似文献
10.
In a series of papers (cf. Bellmanet al., 1965a, b; Kagiwadaet al., 1975), an estimation of optical properties of turbid media has been made, in the least-squared sense, with the aid of quasi-linearization and invariant imbedding. Recently, an extension of the above procedure to the three-dimensional case with horizontally inhomogeneous albedo of the underlying surface has been attempted (Ueno, 1982). From computational aspects the numerical evaluation is not so easy, even by means of high-speed electronic computers. In the present paper it is shown that the latin-square algorithm is a useful estimate for the least-squares inference of the optical properties of turbid media bounded by an inhomogeneous reflecting surface. 相似文献
11.
María del Carmen Martínez Juan F. Navarro José Manuel Ferrándiz 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):59-68
The efficiency in the computation of circular functions, such as cos(u) or sin(u), where u is a Poisson series, is important to derive accurate solutions of many problems of Celestial Mechanics, for instance, the
orbital or rotational perturbed motion of natural or artificial bodies, since expansions in terms of Legendre functions and
multiple Fourier series appear almost everywhere. Therefore, it is worth searching for alternative algorithms with lower computational
cost. In this article, we propose a method based on the idea of elimination, which was originally applied to solve numerical
problems, mainly in the case of matrix functions. Our comparisons with the traditional Taylor expansion prove that this new method can be more efficient when applied to compute the sine and cosine of a Poisson series. 相似文献
12.
In this paper a slightly different approach is proposed for the process of determining the functions S
m
and H
m
* of the algorithm of the canonical version of Hori method. This process will be referred to as integration theory of the mth order equation of the method. It will be shown that the ordinary differential equation with an auxiliary parameter t
* as independent variable, introduced through Hori auxiliary system, can be replaced by a partial differential equation in the time t. In this way, the mth order equation of the algorithm assumes a form very similar to the one of other perturbation methods. In virtue of this new approach of the integration theory for Hori method, Lagrange's variational equations introduced by Sessin are revised. As an example, the Duffing equation is solved through this new approach. 相似文献
13.
Recently observed oscillations in the solar atmosphere have been interpreted and modeled as magnetohydrodynamic wave modes.
This has allowed for the estimation of parameters that are otherwise hard to derive, such as the coronal magnetic-field strength.
This work crucially relies on the initial detection of the oscillations, which is commonly done manually. The volume of Solar Dynamics Observatory (SDO) data will make manual detection inefficient for detecting all of the oscillating regions. An algorithm is presented
that automates the detection of areas of the solar atmosphere that support spatially extended oscillations. The algorithm
identifies areas in the solar atmosphere whose oscillation content is described by a single, dominant oscillation within a
user-defined frequency range. The method is based on Bayesian spectral analysis of time series and image filtering. A Bayesian
approach sidesteps the need for an a-priori noise estimate to calculate rejection criteria for the observed signal, and it also provides estimates of oscillation frequency,
amplitude, and noise, and the error in all of these quantities, in a self-consistent way. The algorithm also introduces the
notion of quality measures to those regions for which a positive detection is claimed, allowing for simple post-detection discrimination by the user.
The algorithm is demonstrated on two Transition Region and Coronal Explorer (TRACE) datasets, and comments regarding its suitability for oscillation detection in SDO are made. 相似文献
14.
V. A. Shefer 《Solar System Research》2010,44(3):252-266
The classic problem of finding the orbit of a celestial body from its two position vectors for two instants of time is considered.
A solution to the problem free from uncertainties is obtained which can be applied for all three kinds of Keplerian movement.
The main part of the computational procedure is reduced to solving one equation with one unknown. Formulas are derived for
the initial value of the equation root, which makes the application of the Newton-Raphson method successful. The efficiency
and reliability of the suggested algorithm is illustrated by examples of the orbit determination for the asteroids Adeona
and Icarus, as well as for Halley’s Comet and Bowell’s Comet. 相似文献
15.
In this paper, we developed statistical method for distance determination of a stellar group. The method depends on the assumption that, the stars scatter around a mean magnitude in a Gaussian distribution. The mean apparent magnitude of the stars is then expressed in terms of the frequency function of the apparent magnitudes, so as to correct for observational incompleteness at the faint end. The problem reduces to the solution of a highly transcendental equation for a given apparent magnitude parameter α. Computational algorithm of the method is illustrated and the numerical solutions of the basic equation are given for some values of α . 相似文献
16.
The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary
missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail
of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories
for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding
process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions
to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded
computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods
perform the terminal fine tuning of the optimization parameters. 相似文献
17.
Preliminary orbit determination is a multipoint boundary value problem which may be solved by the generalized Newton-Raphson iteration. When applied formally the method suffers from extensive computer storage requirements, fairly long execution times and in some cases, insufficient accuracy. In this work we seek to remove these practical difficulties via modification of the computational algorithm in such a way that solution storage is eliminated for the most part and computational speed and tolerance to imprecise integration algorithms is improved. The modified methods are applied to nine typical preliminary orbit determination problems to demonstrate fast convergence and short computation times, even with very poor starting values for the iteration. Excellent precision of the resulting solution is also demonstrated as well as the algorithm's ability to handle circular, elliptic, parabolic and hyperbolic orbits. 相似文献
18.
The SMF algorithms were recently developed by the authors as a multistep generalization of the ScheifeleG-functions one-step method. Like the last, the proposed codes integrate harmonic oscillations without truncation error and the perturbing parameter appears as a factor of that error when integrating perturbed oscillations. Therefore they seemed to be convenient for the accurate integration of orbital problems after the application of linearizing transformations, such as KS or BF. In this paper we present several numerical experiments concerning the propagation of Earth satellite orbits, that illustrate the performance of the the SMF method. In general, it provides greater accuracy than the usual standard algorithms for similar computational cost. 相似文献
19.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1981,78(2):359-400
In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofG will be established for anyx
i; withn, N positive integers and |i|<1 fori=1, 2, ... n. Moreover, the recurrence formulae satisfied by these coefficients will also be established. Illustrative analytical examples and a full recursive computational algorithm, with its numerical results, are included. The applications of the recurrence formulae are also illustrated by their stencils. As by-products of the analyses are two important periodic integrals developed analytically and computationally. 相似文献
20.
L. Miller T. D. Kitching C. Heymans A. F. Heavens L. Van Waerbeke 《Monthly notices of the Royal Astronomical Society》2007,382(1):315-324
The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing measurement with maximal signal-to-noise ratio, coupled with estimation of measurement errors. The distinction between likelihood-based and Bayesian methods is discussed. Systematic biases in the Bayesian method may be evaluated as part of the fitting process, and overall such an approach should yield unbiased shear estimation without requiring external calibration from simulations. The principal disadvantage of model fitting for large surveys is the computational time required, but here an algorithm is presented that enables large surveys to be analysed in feasible computation times. The method and algorithm is tested on simulated galaxies from the Shear TEsting Programme (STEP). 相似文献