共查询到20条相似文献，搜索用时 15 毫秒
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Methods of iteration are discussed in relation to Kepler's equation, and various initial guesses are considered, with possible strategies for choosing them. Several of these are compared; the method of iteration used in the comparisons has local convergence of the fourth order.WANG Laboratories, Inc. 相似文献
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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
4.
The construction of model atmospheres by means of differential corrections is discussed. Either flux or flux gradients may be minimized, with arbitrary weighting with depth. For the simple atmospheres studied, no convergence problems were encountered even when very poor first approximations were used; and flux constancy in the radiative case was generally attained in three or four iterations.Quantities computed in one iteration may be re-used, not only in subsequent iterations within the model, but also in the construction of other models with differentT
eff org; and so the method is particularly suited for grid computations. 相似文献
5.
An analytical approach to small amplitude solutions of the extended nearly circular Sitnikov problem
J. Hagel 《Celestial Mechanics and Dynamical Astronomy》2009,103(3):251-266
The model of extended Sitnikov Problem contains two equally heavy bodies of mass m moving on two symmetrical orbits w.r.t the centre of gravity. A third body of equal mass m moves along a line z perpendicular to the primaries plane, intersecting it at the centre of gravity. For sufficiently small distance from the
primaries plane the third body describes an oscillatory motion around it. The motion of the three bodies is described by a
coupled system of second order differential equations for the radial distance of the primaries r and the third mass oscillation z. This problem which is dealt with for zero initial eccentricity of the primaries motion, is generally non integrable and
therefore represents an interesting dynamical system for advanced perturbative methods. In the present paper we use an original
method of rewriting the coupled system of equations as a function iteration in such a way as to decouple the two equations
at any iteration step. The decoupled equations are then solved by classical perturbation methods. A prove of local convergence
of the function iteration method is given and the iterations are carried out to order 1 in r and to order 2 in z. For small values of the initial oscillation amplitude of the third mass we obtain results in very good agreement to numerically
obtained solutions. 相似文献
6.
A. Peraiah 《Journal of Astrophysics and Astronomy》1980,1(2):101-111
A direct iteration has been performed to obtain a simultaneous solution of the equations of line transfer in an expanding
spherically symmetric atmosphere in the comoving frame with statistical equilibrium for a non-LTE, two-level atom. The solution
converges in three or four iterations to an accuracy of 1 per cent of the ratio of the population densities of the two levels.
As initial values, the upper level population was set equal to zero or to the LTE densities. The final solution on convergence
indicates enhanced population of these levels over the initial values assumed, Large velocity gradients enhance this effect
whereas large geometrical sizes of the atmospheres tend to reduce it. 相似文献
7.
We review starting formulae and iteration processes for the solution of Kepler's equation, and give details of two complete procedures. The first has been in use for a number of years, but the second is entirely new. The new procedure operates with an iterative process that always gives fourth-order convergence and is taken to only two iterations. The error in the resulting solution then never exceeds 7×10–15 rad. 相似文献
8.
D. I. Nagirner 《Astrophysics》1994,37(1):69-78
A new method is presented for calculating spectral line radiation transport in a homogeneous circular cylinder with infinitely long axis for isotropic scattering with complete frequency redistribution or no change in frequency. In addition to the cylinder, scattering in a layer symmetric about its midpoint and in a sphere are also studied. Equations are derived which are satisfied by the resolvent of the fundamental integral equation describing these cases of scattering. By applying a Hankel transform over a finite interval, the resolvent is expressed in terms of an auxiliary function. An equation is derived for this auxiliary function which is easily soluble by iteration, with the speed of its convergence increasing with growth in the radius of the scattering region.Translated from Astrofizika, Vol. 37, No. 1, pp. 111–127, January–March, 1994.This study was carried out with financial support from the Russian Fund for Fundamental Studies (project 93-02-2957). 相似文献
9.
The unit vector method (PUVM1) by which the observed data of artificial satellites are used to determine the perturbed initial orbits has been widely applied. In order to further perfect and improve this method, first, a mathematical model (MMUVM) corresponding to this method is constructed on the basis of measuring errors. In essence, the MMUVM is a nonlinear optimization problem. In the light of the MMUVM, simulated and observed data of multiple circuits are taken to form specific objective functions, which are then processed by means of a direct search method and with of a tri-diagonal quadratic interpolation model for solving optimization problems. The calculated results show that the optimization model MMUVM is right and reasonable and the adopted direct method is practical and effective. Secondly, the relation between PUVM1 and MMUVM is further clarified: PUVM1 is essentially a simplified form of the MMUVM, and the primary reason is found from mathematical principles, why it is that PUVM1 can only be applied to short-arc data within one circuit and not to long-arc or multi-circuit data. Finally, a preliminary theoretical analysis of the convergence of the iteration algorithm of PUVM1 is carried out and instancesof numerical verification given. It is pointed out that the iterative scheme of PUVM1 is conditionally convergent. This means that sometimes, even though the quasi-normalization equation is reasonable, the iteration diverges. 相似文献
10.
Lunar Orbital Station (LOS) is proposed as support of manned lunar exploration missions. A fast-converging iteration method for determining the initial conditions of two-impulse transfer trajectories between the Earth and the LOS is proposed based on the patched conic approach. In the Earth phase, near Earth state is connected with the state at the lunar sphere of influence (LSOI) based on the relationship between the initial and terminal orbital state. Then, an analytical algorithm is proposed to find the state vector at LSOI, such to satisfy the LOS orbital constraint. An iterative process is finally adopted to generate favorable initial solutions that satisfy the constraint near the Earth and at the perilune. The algorithm convergence is investigated, and two types of transfer trajectories are found for both Earth-LOS and LOS-Earth transfer. Based on the algorithm, orbital transfer windows, velocity impulse and time of flight are analyzed in the typical years 2025 and 2034. At last, the initial solution is corrected with a high fidelity model based on the active-set method, which shows the precision of this algorithm. The novel procedure for the transfer trajectories design and the analytic result can be used as a basis for rapid mission evaluation and design for future manned lunar missions based on the LOS. 相似文献
11.
在间接法求解小推力轨道计算中,通过先选取合适的性能指标,并对小推力最优控制问题转化为两点边值问题的方程在开普勒轨道附近线性展开,有效增强了协态变量初值收敛性,使得该方法无需对协态变量初值进行反复的随机猜测,迭代过程也不需要人工干预,提高了轨道搜索应用中的计算效率.之后再对性能指标进行迭代优化,可获得逼近于Bang-bang控制的控制方案. 相似文献
12.
S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》1994,58(1):37-52
A computer-assisted reformulation of Sundman's determination of the the domain of absolute convergence of the Laplacian expansion fo the disturbing function is given. Sundman's results are extended to the cases of librating perihelions and a convergence criterion is established for the case of mutually inclined orbits. 相似文献
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针对LAMOST (Large Sky Area Multi-Object Fiber Spectroscopic Telescope)2维光谱图像数据,对6种抽谱算法进行了分析与比较.比较的算法包括孔径法、轮廓拟合法、直接反卷积方法、基于Tikhonov正则化的反卷积抽谱算法、基于自适应Landweber迭代的反卷积抽谱算法以及基于Richardson-Lucy迭代的反卷积抽谱算法.通过实验对这些算法在信噪比和分辨率两个方面进行了比较,发现基于Tikhonov正则化的反卷积抽谱算法、基于自适应Landweber迭代的反卷积抽谱算法以及基于RichardsonLucy迭代的反卷积抽谱算法是6种算法中最为可靠的3种抽谱算法.最后,对今后的工作进行了展望. 相似文献
14.
《Chinese Astronomy and Astrophysics》1984,8(1):47-49
The trigonometric parallex of BD +2°348 is derived using the central overlap iteration algorithm. The result is 0″.0879± 0″.0178. 相似文献
15.
We have obtained a simultaneous solution of the statistical equilibrium equation for a non-LTE two-level atom and the radiative transfer equation in the comoving frames by employing the angle-averaged partial frequency redistribution.R
i
with isotropic scattering. In the first iteration we have set the population density of the upper level equal to zero and allow it to be populated in the subsequent iterations. The solution converges within two to four iterations. The process of iteration is terminated when the ratios of population densities in two successive iterations at each radial point, attain an accuracy of 1%. The effects of partial frequency redistribution is to increase the population density of the upper level. Radial gas motions do not seem to have significant effects, although in highly extend geometries, velocity gradients change the population densities considerably. 相似文献
16.
M. S. Wheatland 《Solar physics》2006,238(1):29-39
Existing methods for calculating nonlinear force-free magnetic fields are slow, and are likely to be inadequate for reconstructing
coronal magnetic fields based on high-resolution vector magnetic field data from a new generation of spectro-polarimetric
instruments. In this paper a new implementation of the current-field iteration method is presented, which is simple, fast,
and accurate. The time taken by the method scales as N
4, for a three-dimensional grid with N
3 points. The method solves the field-updating part of the iteration by exploiting a three-dimensional Fast Fourier Transform
solution of Ampere’s law with a current density field constructed to satisfy the required boundary conditions, and uses field
line tracing to solve the current-updating part of the iteration. The method is demonstrated in application to a known nonlinear
force-free field and to a bipolar test case. 相似文献
17.
Egemen Kolemen N. Jeremy Kasdin Pini Gurfil 《Celestial Mechanics and Dynamical Astronomy》2012,112(1):47-74
A new fully numerical method is presented which employs multiple Poincaré sections to find quasiperiodic orbits of the Restricted
Three-Body Problem (RTBP). The main advantages of this method are the small overhead cost of programming and very fast execution
times, robust behavior near chaotic regions that leads to full convergence for given family of quasiperiodic orbits and the
minimal memory required to store these orbits. This method reduces the calculations required for searching two-dimensional
invariant tori to a search for closed orbits, which are the intersection of the invariant tori with the Poincaré sections.
Truncated Fourier series are employed to represent these closed orbits. The flow of the differential equation on the invariant
tori is reduced to maps between the consecutive Poincaré maps. A Newton iteration scheme utilizes the invariance of the circles
of the maps on these Poincaré sections in order to find the Fourier coefficients that define the circles to any given accuracy.
A continuation procedure that uses the incremental behavior of the Fourier coefficients between close quasiperiodic orbits
is utilized to extend the results from a single orbit to a family of orbits. Quasi-halo and Lissajous families of the Sun–Earth
RTBP around the L2 libration point are obtained via this method. Results are compared with the existing literature. A numerical
method to transform these orbits from the RTBP model to the real ephemeris model of the Solar System is introduced and applied. 相似文献
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We review large scale modelling of the ISM with emphasis on the importance to include the disk-halo-disk duty cycle and to use a dynamical refinement of the grid (in regions where steep variations of density and pressure occur) for a realistic modelling of the ISM. We also discuss the necessity of convergence of the simulation results by comparing 0.625, 1.25 and 2.5 pc resolution simulations and show that a minimum grid resolution of 1.25 pc is required for quantitatively reliable results, as there is a rapid convergence for Δ × ≤ 1.1 pc. 相似文献
20.
《New Astronomy》2022
We numerically investigate the effect of oblateness parameter on the topology of basins of convergence connected with the equilibrium points in the restricted three-body problem when the test particle is an oblate spheroid, and the influence of the gravitational potential from the belt is taken into consideration. Additionally, the primaries are also not spherical in shape, on the contrary, it is oblate or prolate spheroid. The parametric variation of the equilibrium points, their stability, and the regions of possible motion are illustrated as the function of the parameters involved. The domain of convergence, on the several two dimensional planes, are unveiled by applying the bi-variate version of the Newton–Raphson iterative method. In addition, we perform a systematic investigation in an order to show how the used parameters affect the topology as well as the degree of fractality of basins of convergence. Moreover, it is also unveiled that how the region of the convergence is related with the number of the required iterations to achieve the desired accuracy with the corresponding probability distribution. 相似文献