共查询到20条相似文献，搜索用时 46 毫秒
1.
The parameters of L matrices are applied to the numerical integration of regular equations describing the motion of minor bodies in the Solar System. The problem of the optimal choice of the regularizing change of variables is formulated in the context of the numerical integration of the equations of motion using the Runge–Kutta–Fehlberg method. Arbitrary perturbations are taken into account. This problem is completely solved in the case of planar motion. The solution of the optimization problem reduces the amount of computations needed to determine the vector of perturbing accelerations. Results of numerical integrations are given. 相似文献
2.
R. Broucke 《Celestial Mechanics and Dynamical Astronomy》1971,4(1):110-115
A Recurrent Power Series solution is given for the classicalN-body problem. The application to numerical integration is also pointed out. 相似文献
3.
Sergei M. Poleshchikov 《Celestial Mechanics and Dynamical Astronomy》2003,85(4):341-393
The sets of L-matrices of the second, fourth and eighth orders are constructed axiomatically. The defining relations are taken from the regularization of motion equations for Keplerian problem. In particular, the Levi-Civita matrix and KS-matrix are L-matrices of second and fourth order, respectively. A theorem on the ranks of L-transformations of different orders is proved. The notion of L-similarity transformation is introduced, certain sets of L-matrices are constructed, and their classification is given. An application of fourth order L-matrices for N-body problem regularization is given. A method of correction for regular coordinates in the Runge–Kutta–Fehlberg integration method for regular motion equations of a perturbed two-body problem is suggested. Comparison is given for the results of numerical integration in the problem of defining the orbit of a satellite, with and without the above correction method. The comparison is carried out with respect to the number of calls to the subroutine evaluating the perturbational accelerations vector. The results of integration using the correction turn out to be in a favorable position. 相似文献
4.
One of the main difficulties encountered in the numerical integration of the gravitationaln-body problem is associated with close approaches. The singularities of the differential equations of motion result in losses of accuracy and in considerable increase in computer time when any of the distances between the participating bodies decreases below a certain value. This value is larger than the distance when tidal effects become important, consequently,numerical problems are encounteredbefore the physical picture is changed. Elimination of these singularities by transformations is known as the process of regularization. This paper discusses such transformations and describes in considerable detail the numerical approaches to more accurate and faster integration. The basic ideas of smoothing and regularization are explained and applications are given. 相似文献
5.
W. Black 《Celestial Mechanics and Dynamical Astronomy》1973,8(3):357-370
It is shown that in the numerical integration ofN-body problems, as much importance should be given to considerations of the computer programming language to be used as to questions of the accummulation of round-off and truncation error, the stability of the method chosen and the problem being treated. By careful programming processing time may be cut by a factor of 2 or 3 which is an important consideration in extended numerical investigations. The relative usefulness of differing strategies for determining the step size is discussed and in addition the usefulness is shown of treatingN-body problems by a Taylor series method. 相似文献
6.
P. Bretagnon P. Rocher J.-L. Simon 《Celestial Mechanics and Dynamical Astronomy》2001,80(3-4):177-184
The accuracy of the rigid Earth solution SMART97 is 2?μ as over the time interval (1968, 2023), accuracy showed by the comparison with a numerical integration using the positions of the Moon, the Sun, and the planets given by DE403. To obtain a nonrigid Earth solution, we use the transfer function of Mathews et al. (2000) and , to keep the precision of our rigid Earth solution in the computation of the geophysical effects, we apply this transfer function to the Earth's angular velocity vector in order to avoid the inherent approximations of the classical methods. Moreover the perturbations of the third component of the angular velocity vector are taken into account. Lastly, we take into account, in an iterative process, the second order perturbations due to the geophysical effects. The results are compared with the Herring solution (1996) published in the IERS Conventions. 相似文献
7.
In this paper, a literal analytical solution is developed for the abundances differential equations of the helium burning phase in hot massive stars. The abundance for each of the basic elements 4He,12C,16O and 20Ne is obtained as a recurrent power series in time, which facilitates its symbolic and numerical evaluations. Numerical comparison between the present solution and the numerical integration of the differential equations for the abundances show good agreement. 相似文献
8.
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
9.
B. P. Kondratyev 《Solar System Research》2011,45(5):447-458
By the new vector method in a nonlinear setting, a physical libration of the Moon is studied. Using the decomposition method
on small parameters we derive the closed system of nine differential equations with terms of the first and second order of
smallness. The conclusion is drawn that in the nonlinear case a connection between the librations in a longitude and latitude,
though feeble, nevertheless exists; therefore, the physical libration already is impossible to subdivide into independent
from each other forms of oscillations, as usually can be done. In the linear approach, ten characteristic frequencies and
two special invariants of the problem are found. It is proved that, taking into account nonlinear terms, the invariants are
periodic functions of time. Therefore, the stationary solution with zero frequency, formally supposing in the linear theory
a resonance, in the nonlinear approach gains only small (proportional to e) periodic oscillations. Near to zero frequency of a resonance there is no, and solution of the nonlinear equations of physical
libration is stable. The given nonlinear solution slightly modifies the previously unknown conical precession of the Moon’s
spin axis. The character of nonlinear solutions near the basic forcing frequency Ω1, where in the linear approach there are beats, is carefully studied. The average method on fast variables is obtained by
the linear system of differential equations with almost periodic coefficients, which describe the evolution of these coefficients
in a nonlinear problem. From this follows that the nonlinear components only slightly modify the specified beats; the interior
period T ≈ 16.53 days appears 411 times less than the exterior one T ≈ 18.61 Julian years. In particular, with such a period the angle between ecliptic plane and Moon orbit plane also varies.
Resonances, on which other researches earlier insisted, are not discovered. As a whole, the nonlinear analysis essentially
improves and supplements a linear picture of the physical libration. 相似文献
10.
Tõnu Viik 《Earth, Moon, and Planets》1990,49(2):163-175
The discrete ordinale method by Chandrasekhar is used to solve the conservative Milne problem in a homogeneous plane-parallel atmosphere which scatters the radiation according to the Rayleigh-Cabannes law.The approximate solution which is supposed to converge uniformly to an exact one when increasing the order of approximation is obtained explicitly. In addition to a tabulation of the Hopf vector for different factors of depolarization, the extrapolation distance, the values of c, q and the Rubenson degrees of polarization at the limb are given. 相似文献
11.
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
12.
We consider a model that describes the evolution of distant satellite orbits and that refines the solution of the doubly averaged
Hill problem. Generally speaking, such a refinement was performed previously by J. Kovalevsky and A.A. Orlov in terms of Zeipel’s
method by constructing a solution of the third order with respect to the small parameter m, the ratio of the mean motions of the planet and the satellite. The analytical solution suggested here differs from the solutions
obtained by these authors and is closest in form to the general solution of the doubly averaged problem (∼m
2). We have performed a qualitative analysis of the evolutionary equations and conditions for the intersection of satellite
orbits with the surface of a spherical planet with a finite radius. Using the suggested solution, we have obtained improved
analytical time dependences of the elements of evolving orbits for a number of distant satellites of giant planets compared
to the solution of the doubly averaged Hill problem and, thus, achieved their better agreement with the results of our numerical
integration of the rigorous equations of perturbed motion for satellites. 相似文献
13.
Eric Bois 《Celestial Mechanics and Dynamical Astronomy》1986,39(4):309-327
This work aims at finding an analytic solution corresponding to the attitude evolution in space of a satellite submitted to disturbing torques. This paper presents a basic frame applicable to any perturbed rotation satellite, and a method of resolution leading to a formal solution which is given here to the first order. Thus, the main problem is the slow rotation of a body with three unequal axes of inertia, essentially submitted to a dominant solar radiation pressure torque, with the axis pointing far away from a position of equilibrium. The comparison of the results with a numerical integration based upon a HIPPARCOS model is convincing. 相似文献
14.
Extrapolation of the solar magnetic field within the potential-field approximation from full-disk magnetograms 总被引：3，自引：0，他引：3
G.V. Rudenko 《Solar physics》2001,198(1):5-30
This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. The boundary conditions are specified by a distribution on the sphere of the projection of the magnetic field vector into a given direction, i.e., they exactly correspond to the data of daily magnetograms distributed across the full solar disk. It is shown that the solution of this problem exists in the form of a spherical harmonic expansion, and uniqueness of this solution is proved. A conceptual sketch of numerical determination of the harmonic series coefficients is given. The field of application of the method is analyzed with regard to the peculiarities of actual data. Results derived from calculating magnetic fields from real magnetograms are presented. Finally, we present differences in results derived from extrapolating the magnetic field from a synoptic map and a full-disk magnetogram. 相似文献
15.
A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near
a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related
characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem
is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular
orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of
the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the
number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity
increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate
impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are
presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal
non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions
depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each
category of solutions are presented. The region of the boundary values that admit each category of solutions of the related
problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results
are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions
are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler
computations than existing methods, its main contribution may be in establishing a new approach to the more general problem. 相似文献
16.
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
17.
R. A. Broucke 《Celestial Mechanics and Dynamical Astronomy》1994,58(2):99-123
We describe a collection of results obtained by numerical integration of orbits in the main problem of artificial satellite theory (theJ
2 problem). The periodic orbits have been classified according to their stability and the Poincaré surfaces of section computed for different values ofJ
2 andH (whereH is thez-component of angular momentum). The problem was scaled down to a fixed value (–1/2) of the energy constant. It is found that the pseudo-circular periodic solution plays a fundamental role. They are the equivalent of the Poincaré first-kind solutions in the three-body problem. The integration of the variational equations shows that these pseudo-circular solutions are stable, except in a very narrow band near the critical inclincation. This results in a sequence of bifurcations near the critical inclination, refining therefore some known results on the critical inclination, for instance by Izsak (1963), Jupp (1975, 1980) and Cushman (1983). We also verify that the double pitchfork bifurcation around the critical inclination exists for large values ofJ
2, as large as |J
2|=0.2. Other secondary (higher-order) bifurcations are also described. The equations of motion were integrated in rotating meridian coordinates. 相似文献
18.
In the n-body problem a central configuration is formed if the position vector of each particle with respect to the center
of mass is a common scalar multiple of its acceleration vector. We consider the problem: given a collinear configuration of
four bodies, under what conditions is it possible to choose positive masses which make it central. We know it is always possible
to choose three positive masses such that the given three positions with the masses form a central configuration. However
for an arbitrary configuration of four bodies, it is not always possible to find positive masses forming a central configuration.
In this paper, we establish an expression of four masses depending on the position x and the center of mass u, which gives a central configuration in the collinear four body problem. Specifically we show that there is a compact region
in which no central configuration is possible for positive masses. Conversely, for any configuration in the complement of
the compact region, it is always possible to choose positive masses to make the configuration central. 相似文献
19.
This paper discusses the formulation and the numerical integration of large systems of differential equations occurring in the gravitational problem ofn-bodies.Different forms of the pertinent differential equations of motion are presented, and various regularizing and smoothing transformations are compared. Details regarding the effectiveness and the efficiency of the Kustaanheimo-Stiefel and of other methods are discussed. In particular, a method is described in which some of the phase variables are treated in the regularized system and others in the ordinary system. This mixed method of numerical regularization offers some advantages.Several numerical integration techniques are compared. A high order Runge-Kutta method, Steffensen's method, and a finite difference method are investigated, especially with regard to their adaptability to regularization.The role of integrals and integral invariants is displayed in controlling the accuracy of the numerical integration.Numerical results are described with 5, 25 and 500 bodies participating. These examples compare the various integration techniques, several regularization methods and different logics in treating binaries. 相似文献
20.
A. V. Usmanov 《Solar physics》1993,143(2):345-363
An attempt is made to infer parameters of the solar corona and the solar wind by means of a numerical, self-consistent MHD simulation. Boundary conditions for the magnetic field are given from the observations of the large-scale magnetic field at the Sun. A two-region, planar (the ecliptic plane is assumed) model for the solar wind flow is considered. Region I of transonic flow is assumed to cover the distances from the solar surface up to 10R
S (R
S is the radius of the Sun). Region II of supersonic, super-Alfvénic flow extends between 10R
S and the Earth's orbit. Treatment for region I is that for a mixed initial-boundary value problem. The solution procedure is similar to that discussed by Endler (1971) and Steinolfson, Suess, and Wu (1982): a steady-state solution is sought as a relaxation to the dynamic equilibrium of an initial state. To obtain a solution to the initial value problem in region II with the initial distribution of dependent variables at 10R
S (deduced from the solution for region I), a numerical scheme similar to that used by Pizzo (1978, 1982) is applied. Solar rotation is taken into account for region II; hence, the interaction between fast and slow solar wind streams is self-consistently treated. As a test example for the proposed formulation and numerical technique, a solution for the problem similar to that discussed by Steinolfson, Suess, and Wu (1982) is obtained. To demonstrate the applicability of our scheme to experimental data, solar magnetic field observations at Stanford University for Carrington rotation 1682 are used to prescribe boundary conditions for the magnetic field at the solar surface. The steady-state solution appropriate for the given boundary conditions was obtained for region I and then traced to the Earth's orbit through region II. We compare the calculated and spacecraft-observed solar wind velocity, radial magnetic field, and number density and find that general trends during the solar rotation are reproduced fairly well although the magnitudes of the density in comparison are vastly different. 相似文献