共查询到20条相似文献，搜索用时 29 毫秒
1.
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
2.
《天文和天体物理学研究(英文版)》2016,(5)
Stokes inversion calculation is a key process in resolving polarization information on radiation from the Sun and obtaining the associated vector magnetic fields. Even in the cases of simple local thermodynamic equilibrium(LTE) and where the Milne-Eddington approximation is valid, the inversion problem may not be easy to solve. The initial values for the iterations are important in handling the case with multiple minima. In this paper, we develop a fast inversion technique without iterations. The time taken for computation is only 1/100 the time that the iterative algorithm takes. In addition, it can provide available initial values even in cases with lower spectral resolutions. This strategy is useful for a filter-type Stokes spectrograph, such as SDO/HMI and the developed two-dimensional real-time spectrograph(2DS). 相似文献
3.
Keiji Ohtsuki 《Icarus》2006,183(2):373-383
We derive an equation for the evolution of rotational energy of Keplerian particles in a dilute disk due to mutual collisions. Three-dimensional Keplerian motion of particles is taken into account precisely, on the basis of Hill's approximation. The Rayleigh distribution of particles' orbital eccentricities and inclinations, and the Gaussian distribution of their rotation rates are also taken into account. Performing appropriate variable transformation, we show that the equation can be expressed with two terms. The first term, which we call collisional stirring term, represents energy exchange between rotation and random motion via collisions. The second term, which we call rotational friction term, tends to equalize the mean rotational energy of particles with different sizes. The equation can describe the evolution of rotational energy of Keplerian particles with an arbitrary size distribution. We analytically evaluate the rates of stirring and friction for the random kinetic energy and rotational energy due to inelastic collisions, for non-gravitating particles in a dilute disk. Using these results, we discuss equilibrium states in a disk of spinning, non-gravitating Keplerian particles. 相似文献
4.
A new scale transformation to the integrated velocity vector is designed to monitor the accumulation of numerical errors in
several integrals of motion. The scale factor is derived from the least-squares correction that minimizes the sum of the squares
of the errors of these integrals. In order to preserve an invariant, we employ the velocity scaling method for rigorously
satisfying the constraint. When adjusting many constants, the new scheme like other existing methods is valid to typically
reduce the integration errors below those of an uncorrected integrator. Via integral invariant relations, the new method is
also able to treat slowly-varying quantities, such as the Keplerian energy and the Laplace vector, for a perturbed Keplerian
problem or each of multiple bodies in the solar system dynamics. Consequently it does nearly agree with the rigorous dual
scaling method in the sense of drastically improving the integration accuracy. As one of its advantages, the implementation
of the new method is significantly easier than that of other methods. In particular, the method can be simply applied to a
complicated dynamical system with some constraints. 相似文献
5.
The instability of axisymmetric flows of inviscid compressible fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The compressibility is taken into account for a homentropic flow with an adiabatic index varying over a wide range. The problem has been solved for two angular velocity profiles of an initial axisymmetric flow. In the first case, a power-law rotation profile with a finite enthalpy gradient at the flow edges has been specified. For this angular velocity profile, we show that the instability of sonic and surface gravity modes in a nearly Keplerian flow, when a radially variable vorticity exists in the main flow, can be explained by the combined action of the Landau mechanism and mode coupling. We also show that including a radially variable vorticity makes the limiting exponent in the rotation law at which the unstable surface gravity modes vanish dependent on the fluid compressibility. In the second case, a Keplerian rotation law with a quasi-sinusoidal deviation has been specified in such a way that the enthalpy gradient vanished at the flow edges. We have found than the sonic modes are then stabilized and the flow is unstable only with respect to the perturbations that also exist in an incompressible fluid. 相似文献
6.
研究近地小天体的探测机会搜索问题．针对交会型探测任务,通过结合变分理论和状态转移矩阵推导了性能指标关于可调参数的解析偏导数,然后在搜索空间中随机生成初始点,并从这些初始点出发利用解析偏导数寻优,从而得到搜索空间内对应潜在发射机会的全部局部极小值点．此方法既在一定程度上保持了传统搜索方法全局搜索的特点,又克服了传统搜索方法的盲目性,因此计算速度获得很大提高．此外该方法可以对探测机会的搜索精度进行有效地控制． 相似文献
7.
On the Distance Function Between Two Keplerian Elliptic Orbits 总被引：1，自引：0，他引：1
Konstantin V. Kholshevnikov Nikolay N. Vassiliev 《Celestial Mechanics and Dynamical Astronomy》1999,75(2):75-83
The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination
of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of
orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does
not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the
minimal distance between two Keplerian orbits.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
W. E. Williamson 《Celestial Mechanics and Dynamical Astronomy》1972,5(2):174-188
The perturbation method, a numerical method for solving two point boundary value problems (TPBVP), is modified to attempt to improve inherent instability and sensitivity problems associated with the method. The desired solution to the TPBVP is divided into two time intervals. The differential equations required to define a solution to the two point boundary value problem are integrated independently over these shorter segments rather than consecutively over the entire trajectory. The independent integration of the differential equations over approximately half of the trajectory instead of the entire trajectory substantially decreases sensitivity and stability properties associated with the numerical integration. The equations for both time segments can be integrated simultaneously. By this procedure, a system of twice the dimension of the original problem is integrated for a period of time equal to half of the time interval for the original problem. To show the effectiveness of the method, two impulse trajectories which minimize the total velocity increment required to transfer a spacecraft from an Earth orbit into a lunar orbit are calculated. 相似文献
9.
10.
经典的初轨确定方法包括Laplace方法和Gauss方法以及它们的各种变化形式. 除这些经典方法之外, 基于当今光学观测数据的特点, 学者们也陆续提出了一些其他的初轨确定方法, 包括双r (目标距离观测者的距离)方法和可行域方法. 双r方法的一种实现方式是通过猜测某两个时刻(通常是定轨弧段的首、末时刻)目标离观测者的距离, 结合观测者在空间中的位置矢量, 即可求解相应的Lambert弧段作为目标轨道的初始猜测. 进一步, 以其他观测时刻的RMS (Root Mean Square)为优化变量可以改进初始猜测从而确定初轨. 可行域方法则是针对一组初始观测参数(包括赤经、赤纬及其变率), 根据一些初始假设将目标(离观测者的)距离及其变率约束在可行域内, 并通过三角划分逐步逼近的方式寻找到使观测RMS最小的猜测解. 针对一系列模拟观测数据以及实测数据, 将智能优化算法(粒子群算法)应用于这两种初轨方法, 并将结果与改进的Laplace算法的结果进行比较. 由于双r方法不仅可以用于短弧定轨还可用于长弧关联, 所以进一步给出了针对长弧段数据的关联结果. 相似文献
11.
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
12.
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
13.
Once the need for an iterative procedure in order to solve the problem of the formation of spectral lines in the case of a model atom with many energy levels, the sequel is to seek for the most effective form of such an iterative scheme. It is an almost universal is assumed within all the iterative methods for the solution of those radiative transfer problems, in which the transfer equations are coupled to the state of the matter, to take as the input of each step of iterations the values of the opacity coefficients obtained as a result of the previous one. This is, for instance, the procedure used to correct the temperature in the computation of stellar atmosphere models, or that to build the -operator (either the exact or the approximated one) within the Accelerated Lambda Iteration methods. Yet, if we assume, in order to solve the multilevel line transfer problem, that at each step of iterations the line opacities are known, we can express via the statistical equilibrium equations the populations of the energy levels - and consequently the source functions of the relevant spectral lines - as a linear function of the full set of the corresponding mean intensities of the radiation field. Once such linear forms for the source functions, we are able to solve without the need of any further approximation the radiative transfer equations for are obtained lines, now linearly coupled through the above linear forms of the statistical equilibrium equations. This is achieved by means of the Implicit Integral Method that we already presented in a series of previous papers. 相似文献
14.
Abdel-Fattah Attia 《Experimental Astronomy》2016,42(3):343-359
The paper presents an adaptive particle swarm optimization (APSO) as an alternative method to determine the optimal orbital elements of the star η Bootis of MK type G0 IV. The proposed algorithm transforms the problem of finding periodic orbits into the problem of detecting global minimizers as a function, to get a best fit of Keplerian and Phase curves. The experimental results demonstrate that the proposed approach of APSO generally more accurate than the standard particle swarm optimization (PSO) and other published optimization algorithms, in terms of solution accuracy, convergence speed and algorithm reliability. 相似文献
15.
Bhaswati Bhattacharyya Rajaram Nityananda 《Monthly notices of the Royal Astronomical Society》2008,387(1):273-278
We present a simple method for determination of the orbital parameters of binary pulsars, using data on the pulsar period at multiple observing epochs. This method uses the circular nature of the velocity space orbit of Keplerian motion and produces preliminary values based on two one-dimensional searches. Preliminary orbital parameter values are then refined using a computationally efficient linear least-squares fit. This method works for random and sparse sampling of the binary orbit. We demonstrate the technique on (i) the highly eccentric binary pulsar PSR J0514−4002 (the first known pulsar in the globular cluster NGC 1851) and (ii) 47 Tuc T, a binary pulsar with a nearly circular orbit. 相似文献
16.
The motion of two massive particles is considered within the framework of the first post-Newtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closed-form solutions for the Delaunay elements in the phase space are obtained. The bridge between the phase space and the state space of the Lagrangian of the motion is provided by a velocity-dependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions. 相似文献
17.
G. Voyatzis T. Kotoulas J. D. Hadjidemetriou 《Monthly notices of the Royal Astronomical Society》2009,395(4):2147-2156
The 2/1 resonant dynamics of a two-planet planar system is studied within the framework of the three-body problem by computing families of periodic orbits and their linear stability. The continuation of resonant periodic orbits from the restricted to the general problem is studied in a systematic way. Starting from the Keplerian unperturbed system, we obtain the resonant families of the circular restricted problem. Then, we find all the families of the resonant elliptic restricted three-body problem, which bifurcate from the circular model. All these families are continued to the general three-body problem, and in this way we can obtain a global picture of all the families of periodic orbits of a two-planet resonant system. The parametric continuation, within the framework of the general problem, takes place by varying the planetary mass ratio ρ. We obtain bifurcations which are caused either due to collisions of the families in the space of initial conditions or due to the vanishing of bifurcation points. Our study refers to the whole range of planetary mass ratio values [ρ∈ (0, ∞)] and, therefore we include the passage from external to internal resonances. Thus, we can obtain all possible stable configurations in a systematic way. As an application, we consider the dynamics of four known planetary systems at the 2/1 resonance and we examine if they are associated with a stable periodic orbit. 相似文献
18.
A solution to the fixed-time minimum-fuel two-impulse rendezvous problem for the general non-coplanar elliptical orbits is
provided. The optimal transfer orbit is obtained using the constrained multiple-revolution Lambert solution. Constraints consist
of lower bound for perigee altitude and upper bound for apogee altitude. The optimal time-free two-impulse transfer problem
between two fixed endpoints implies finding the roots of an eighth order polynomial, which is done using a numerical iterative
technique. The set of feasible solutions is determined by using the constraints conditions to solve for the short-path and
long-path orbits semimajor axis ranges. Then, by comparing the optimal time-free solution with the feasible solutions, the
optimal semimajor axis for the two fixed-endpoints transfer is identified. Based on the proposed solution procedure for the
optimal two fixed-endpoints transfer, a contour of the minimum cost for different initial and final coasting parameters is
obtained. Finally, a numerical optimization algorithm (e.g., evolutionary algorithm) can be used to solve this global minimization
problem. A numerical example is provided to show how to apply the proposed technique. 相似文献
19.
Stefano Casotto 《Celestial Mechanics and Dynamical Astronomy》2018,130(8):52
The Keplerian differential state transition matrix (KDSTM) is a fundamental tool in investigations of the sensitivity of orbital evolution to changes in initial conditions, in perturbation analysis, as well as in targeting and rendezvous operations. Several different forms of the KDSTM are available in the literature. They differ in the choice of state space variables, as well as in derivation methods. Here, a new method for constructing the KDSTM is presented, which is based on the well-known theorem on the differentiability of the solution of a system of ordinary differential equations with respect to initial conditions. A peculiarity of the method is that it allows the direct construction of analytical expressions for both the direct and the inverse fundamental matrices needed to form the KDSTM. The KDSTM is first built in the inertial reference frame and then transformed to the orbital, or Hill reference frame. The resulting expressions contain the full set of Keplerian elements and are hence readily extensible to perturbed Keplerian reference motion. The results are compared with some of the best known KDSTM’s available in the literature, with which they are proven to be fully equivalent, despite their sometimes dramatically different appearance. 相似文献
20.
Abdel-Fattah Attia 《Astrophysics and Space Science》2011,334(1):103-114
This paper presents an ‘adaptive probability of crossover’ technique, as a variation of the differential evolution algorithm
(ACDE), for optimal parameter estimation in the general curve-fitting problem. The technique is applied to the determination
of orbital elements of a spectroscopic binary system (eta Bootis). In the ACDE, Varying the crossover probability rate (Cr) provides faster convergence than keeping it constant. The Cr is determined for each trial parameter vector (‘individual’) as a function of fit goodness. The adaptation automatically
updates control parameter to an appropriate value, without requiring prior knowledge of the relationship between particular
parameter settings and a given problem optimization characteristics. The presented analysis of eta Bootis derives best-fitting
Keplerian and phasing curves. Error estimation of the optimal parameters is also included. Comparison of the results with
previously published values suggests that the ACDE technique has a useful applicability to astrophysical data analysis. 相似文献