共查询到20条相似文献，搜索用时 31 毫秒
1.
The problem of diffuse reflection and transmission of solar radiation through a planetary atmosphere bounded from below by a reflecting surface is solved. The solution method based on rewriting the solution of the proposed problem in terms of the well known standard problem solution, where the planetary surface does not reflect. The solution of the standard problem can be found elsewhere or as we did by using the maximum entropy method. Numerical results for the angular radiation intensity and for the reflection and transmission coefficients are presented and compared with those obtained by Chandrasekhar's method. 相似文献
2.
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
3.
S. B. Faruque 《Celestial Mechanics and Dynamical Astronomy》2003,87(4):353-369
A new analytic expression for the position of the infinitesimal body in the elliptic Sitnikov problem is presented. This solution is valid for small bounded oscillations in cases of moderate primary eccentricities. We first linearize the problem and obtain solution to this Hill's type equation. After that the lowest order nonlinear force is added to the problem. The final solution to the equation with nonlinear force included is obtained through first the use of a Courant and Snyder transformation followed by the Lindstedt–Poincaré perturbation method and again an application of Courant and Snyder transformation. The solution thus obtained is compared with existing solutions, and satisfactory agreement is found. 相似文献
4.
Lambert problem solution in the hill model of motion 总被引：1，自引：0，他引：1
Alexander Sukhanov Antonio F. Bertachini A. Prado 《Celestial Mechanics and Dynamical Astronomy》2004,90(3-4):331-354
The goal of this paper is obtaining a solution of the Lambert problem in the restricted three-body problem described by the
Hill equations. This solution is based on the use of pre determinate reference orbits of different types giving the first
guess and defining the sought-for transfer type. A mathematical procedure giving the Lambert problem solution is described.
This procedure provides step-by-step transformation of the reference orbit to the sought-for transfer orbit. Numerical examples
of the procedure application to the transfers in the Sun–Earth system are considered. These examples include transfer between
two specified positions in a given time, a periodic orbit design, a halo orbit design, halo-to-halo transfers, LEO-to-halo
transfer, analysis of a family of the halo-to-halo transfer orbits. The proposed method of the Lambert problem solution can
be used for the two-point boundary value problem solution in any model of motion if a set of typical reference orbits can
be found. 相似文献
5.
论述的短弧定轨,是指在无先验信息情况下又避开多变元迭代的初轨计算方法,它需要相应的动力学问题有一能反映短弧内达到一定精度的近似分析解．探测器进入月球引力作用范围后接近月球时可以处理成相对月球的受摄二体问题,而在地球附近,则可处理成相对地球的受摄二体问题,但在整个过渡段的力模型只能处理成一个受摄的限制性三体问题．而限制性三体问题无分析解,即使在月球引力作用范围外,对于大推力脉冲式的过渡方式,相对地球的变化椭圆轨道的偏心率很大(超过Laplace极限),在考虑月球引力摄动时亦无法构造摄动分析解．就此问题,考虑在地球非球形引力(只包含J2项)和月球引力共同作用下,构造了探测器飞抵月球过渡轨道段的时间幂级数解,在此基础上给出一种受摄二体问题意义下的初轨计算方法,经数值验证,定轨方法有效,可供地面测控系统参考． 相似文献
6.
Mayer's variational problem for a point with a limited mass flow rate is described by differential equations of the fourteenth order, allowing for a few first integrals. By reducing the equations to closed canonical form, these integrals are analyzed from the viewpoint of finding a possible solution to the problem via quadratures on zero, intermediate, and maximum thrust sections. In addition to confirming well-known cases of total integrability, this approach enabled us to establish that the essential difficulty of the solution of the space problem with intermediate thrust is reduced to finding one integral, and the solution of the problem with maximum thrust requires two integrals in involution. It is shown that these integrals can be applied to find particular solutions. 相似文献
7.
Diana P. Kjurkchieva 《Astrophysics and Space Science》1987,138(1):141-145
On the basis of the analytical solution of the direct photometric problem for spotted stars is obtained solution of the corresponding inverse problem. It is given expressions for determining of the location, size, and temperature of the spot and of the inclination of the rotational axis of the spotted star with regard to the line-of-sight. 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.
Diarmuid O'Mathuna 《Celestial Mechanics and Dynamical Astronomy》1970,1(3-4):467-478
For Vinti's dynamical problem, there is proposed a new form of solution wherein all three coordinates are expressed in terms of one independent variable. The formulae for the three co-ordinates are clear generalizations of the corresponding formulae for the Kepler problem while the independent variable corresponds to the true anomaly. The solution is completed by the relation connecting the independent variable with time: the latter is a generalization of the well known Kepler time-angle relationship. From the form and method of solution the main qualitative features of the motion are readily derived. 相似文献
10.
Sukanta Bose 《Journal of Astrophysics and Astronomy》1997,18(4):381-387
We briefly review the status of the “graceful exit” problem in superstring cosmology and present a possible resolution. It
is shown that there exists a solution to this problem in two-dimensional dilaton gravity provided quantum corrections are
incorporated. This is similar to the recently proposed solution of Rey. However, unlike in his case, in our one-loop corrected
model the graceful exit problem is solved for any finite number of massless scalar matter fields present in the theory. 相似文献
11.
V. Papoyan 《Astrophysics and Space Science》1986,124(2):335-344
The problem of stationary axisymmetric gravitational fields is formulated within the framework of Generalized Theory of Gravitation. It is shown that solutions of the problem mentioned above may be found, if analogous solutions in General Relativity are obtained. As an illustration a Kerr-like solution is offered. A generation theorem for finding magnetostatic solution from stationary vacuum solutions is proposed. 相似文献
12.
Homotopy methods have been widely utilized to solve low-thrust orbital transfer problems, however, it is not guaranteed that the optimal solution can be obtained by the existing homotopy methods. In this paper, a new homotopy method is presented, by which the optimal solution can be found with probability one. Generalized sufficient conditions, which are derived from the parametrized Sard’s theorem, are first developed. A new type of probability-one homotopy formulation, which is custom-designed for solving minimum-time low-thrust trajectory optimization problems and satisfies all these sufficient conditions, is then constructed. By tracking the continuous zero curve initiated by an initial problem with known solution, the optimal solution of the original problem is guaranteed to be solved with probability one. Numerical demonstrations in a three-dimensional time-optimal low-thrust orbital transfer problem with 43 revolutions is presented to illustrate the applications of the method. 相似文献
13.
Bruce A. Conway 《Celestial Mechanics and Dynamical Astronomy》1986,39(2):199-211
A root-finding method due to Laguerre (1834–1886) is applied to the solution of the Kepler problem. The speed of convergence of this method is compared with that of Newton's method and several higher-order Newton methods for the problem formulated in both conventional and universal variables and for both elliptic and hyperbolic orbits. In many thousands of trials the Laguerre method never failed to converge to the correct solution, even from exceptionally poor starting approximations. The non-local robustness and speed of convergence of the Laguerre method should make it the preferred method for the solution of Kepler's equation. 相似文献
14.
Two-point boundary value problems appear frequently in space trajectory design. A remarkable example is represented by the
Lambert’s problem, where the conic arc linking two fixed positions in space in a given time is to be characterized in the
frame of the two-body problem. Classical methods to numerically solve these problems rely on iterative procedures, which turn
out to be computationally intensive in case of lack of good first guesses for the solution. An algorithm to obtain the high
order expansion of the solution of a two-point boundary value problem is presented in this paper. The classical iterative
procedures are applied to identify a reference solution. Then, differential algebra is used to expand the solution of the
problem around the achieved one. Consequently, the computation of new solutions in a relatively large neighborhood of the
reference one is reduced to the simple evaluation of polynomials. The performances of the method are assessed by addressing
typical applications in the field of spacecraft dynamics, such as the identification of halo orbits and the design of aerocapture
maneuvers. 相似文献
15.
The quasisimilar theory is used to investigate the solution of the blast wave problem with generalized geometries in a non-ideal
gas satisfying the equation of state of the Van der Waals type. Here it is assumed that the distribution of normalized velocity,
pressure and density are nearly similar in the narrow range of the shock strength. A comparison between approximate analytical
solution and numerical solution of the problem is presented for the cylindrical geometry. The numerical solutions are presented
for the generalized geometry in a non-ideal gas. It is also assessed as to how the non-idealness of the gas affects the behavior
of the flow parameters. 相似文献
16.
Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1981,24(4):377-390
An asymptotic solution for the cylindrical coordinates of Trojan asteroids is derived by using a three-variable expansion method in the elliptic restricted three-body problem. The perturbations of the orbital elements are obtained from this solution by applying the formulas of the two-body problem. The main perturbations of the mean motion are studied in detail. 相似文献
17.
M. J. Miketinac 《Astrophysics and Space Science》1984,106(1):151-160
A numerical method for the solution of the (astrophysical) potential problem is presented. The problem is formulated as a free boundary problem for a mildly nonlinear elliptic partial differential equation and the method is obtained by combining Newton-Raphson's procedure and two different types of discretization. The performance of the method is discussed. 相似文献
18.
D. Pelat 《Monthly notices of the Royal Astronomical Society》1998,299(3):877-888
In order to derive the stellar population of a galaxy or a star cluster, it is a common practice to fit its spectrum by a combination of spectra extracted from a data base (e.g. a library of stellar spectra). If the data to be fitted are equivalent widths, the combination is a non-linear one and the problem of finding the 'best' combination of stars that fits the data becomes complex. It is probably because of this complexity that the mathematical aspects of the problem did not receive a satisfying treatment; the question of the uniqueness of the solution , for example, was left in uncertainty. In this paper we complete the solution of the problem by considering the underdetermined case where there are fewer equivalent widths to fit than stars in the data base (the overdetermined case was treated previously). The underdetermined case is interesting to consider because it leaves space for the addition of supplementary astrophysical constraints. In fact, it is shown in this paper that when a solution exists it is generally not unique. There are infinitely many solutions, all of them contained within a convex polyhedron in the solutions vector space. The vertices of this polyhedron are extremal solutions of the stellar population synthesis. If no exact solution exists, an approximate solution can be found using the method described for the overdetermined case. Also provided is an algorithm able to solve the problem numerically; in particular all the vertices of the polyhedron are found. 相似文献
19.
George A. Tsirogiannis 《Celestial Mechanics and Dynamical Astronomy》2012,114(4):353-363
A space mission design methodology is presented, where initial and final orbits are connected through segments of periodic orbits. After a discretization of the solution space, the problem of mission design is transformed into an equivalent combinatorial optimization problem. Specifically, a graph is constructed that represents periodic orbits connected by the execution of impulsive maneuvers. A low computational complexity algorithm for this transformation is introduced. An efficient combinatorial optimization algorithm that solves the shortest path problem is described. Subject to the initial discretization of the solution space, an optimal sequence of coastal arcs is determined for a low total Delta-V mission. Finally, the proposed methodology is applied to the design of a hypothetical Saturn?CTitan system mission. 相似文献
20.
A theory is constructed for solving half-space, boundary-value problems for the Chandrasekhar equations, describing the propagation
of polarized light, for a combination of Rayleigh and isotropic scattering, with an arbitrary probability of photon survival
in an elementary act of scattering. A theorem on resolving a solution into eigenvectors of the discrete and continuous spectra
is proven. The proof comes down to solving a vector, Riemann—Hilbert, boundary-value problem with a matrix coefficient, the
diagonalizing matrix of which has eight branching points in the complex plane. Isolation of the analytical branch of the diagonalizing
matrix enables one to reduce the Riemann—Hilbert problem to two scalar problems based on a [0, 1] cut and two vector problems
based on an auxiliary cut. The solution of the Riemann—Hilbert problem is given in the class of meromorphic vectors. The conditions
of solvability enable one to uniquely determine the unknown expansion coefficients and free parameters of the solution of
the boundary-value problem.
Translated from Astrofizika, Vol. 41, No. 2, pp. 263–276, April-June, 1998. 相似文献