共查询到20条相似文献，搜索用时 31 毫秒
1.
D. I. Nagirner 《Astrophysics》1995,38(1):39-47
We present a method for computing the spectrum of the integral equation for radiation transfer in a cylinder. This method, as in the previous articles in this series, is based on a Hankel transformation applied to the equation. Calculating the spectrum then reduces to solving the equation for the auxiliary function for each eigenvalue separately. The corresponding eigenfunction is then found by an additional integration. We find asymptotic expressions for the eigenvalues and the eigenfunctions for a cylinder with a large optical radius when there is scattering in a spectral line, with complete redistribution over frequency when the absorption coefficient obeys a power law. We also derive equations determining the quantities entering into these expressions. For the simplest kernel of the equation all quantities can be expressed in terms of Bessel functions and roots of a transcendental equation.Translated from Astrofizika, Vol. 38, No. 1, pp. 75–88, January–March, 1995. 相似文献
2.
Vinti’s potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti’s spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating \(J_2\), \(J_3\), and generally a partial \(J_4\) in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti’s solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti’s solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti’s solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the \(J_2\) through \(J_5\) terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim–Alfriend state transition matrix, which considers the \(J_2\) perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material. 相似文献
3.
轨道改进中计算状态转移矩阵的分析方法 总被引：1，自引：0，他引：1
对当今人卫轨道改进问题,由于力学模型的复杂,精密星历和状态转移矩阵的计算均采用数值方法,这就需要积分两组常微分方程．本文针对状态转移矩阵在定轨中的作用,对定轨弧段不太长的情况,给出了状态转移矩阵的一种分析算法,从而避免数值求解两组常微分方程的问题,并以实际算例证实了这种算法的有效性 相似文献
4.
A new simple method for the closed-form solution of nonlinear algebraic and transcendental equations through integral formulae is proposed. This method is applied to the solution of the famous Kepler equation in the two-body problem for elliptic orbits. The resulting formulae are quite elementary and, beyond their analytical interest, they can also provide quite accurate numerical results by using Gausstype quadrature rules. 相似文献
5.
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
6.
A new second-order solution to the two-point boundary value problem for relative motion about orbital rendezvous in one orbit
period is proposed. First, nonlinear differential equations to describe the relative motion between a chaser and a target
are presented considering the second-order terms in the gravity. Then, by regarding the second-order terms as external accelerations,
we establish second-order state transition equations. Moreover, the J2 perturbations effects can also be considered in the
state transition equations. Last, the initial relative velocity to fulfill a rendezvous is determined by solving the state
transition equations. Numerical simulations show that the new second-order state transition equations are accurate. The second-order
solution to the two-point boundary value problem on eccentric orbits is valid even if the relative range is farther than 500 km. 相似文献
7.
N. Borderies 《Celestial Mechanics and Dynamical Astronomy》1977,16(3):291-308
This paper deals with the Adams-Moulton-Cowell multistep integrator, as described by Oestwinter and Cohen (1972). In order to evaluate the accuracy of the method, we started to test it in the case of the unperturbed two-body motion; numerical instability may arise by integrating first order systems. The accuracy is improved by applying a Sundmann transformation of the independent variable. The algorithm is then modified such that the equations of pure keplerian motion are integrated with respect to the new independent variable without truncation error; numerical experiments show the considerable improvement of accuracy and the reduction of computing time for Keplerian motion.If terms of the disturbing function of the Earth are added to the central potential, the time-transformation is less effective. With a modification of this time-transformation as given by Moynot in 1971, it is possible to reduce the propagation of the truncation error in the J2 problem. 相似文献
8.
J. Kriz 《Celestial Mechanics and Dynamical Astronomy》1978,18(4):371-382
The uniform valid state transition matrix of the pure Keplerian motion is established by means of the KS-transformation. Perturbed interplanetary transfer- and flyby-problems are treated by integrating the perturbed trajectory numerically and by performing the differential correction technique using the analytical transition matrix of the unperturbed motion. Numerical examples show the efficiency of this procedure and the improvement of the computing time and accuracy in comparison with the shooting method. 相似文献
9.
S. I. Grachev 《Astrophysics》2000,43(1):70-86
In the first of the series of papers by Ivanov et al. it was shown that the model problem of the transfer of polarized radiation as a result of resonance scattering from two-level atoms in a homogeneous plane atmosphere in the absence of LTE comes down, in the approximation of complete frequency redistribution, to the solution of an integral matrix equation of the Wiener-Hopf type for a (2 × 2) matrix source function S(τ). In the second paper in this series, devoted to the vector Milne problem, complete asymptotic expansions of the matrix I(z) [which is essentially a Laplace transform of the matrix S(τ)] for the case of a Doppler profile of the coefficient of absorption, and the coefficients of asymptotic expansions of S(τ) (τ » 1) are expressed in terms of coefficients of the expansions of I(z). We show that asymptotic expansions of S(τ) can be found directly from an integral matrix equation of the Wiener-Hopf type for S(τ). We give new recursive equations for the coefficients of these expansions, as well as a new derivation of asymptotic expansions of the matrix I, including its second column, which was considered only briefly by Ivanov et al. 相似文献
10.
This note gives a concise algorithm for computing a normal form for a real linear Hamiltonian differential equatin which has purely imaginary eigenvalues. This algorithm is then applied to the differential equation which comes from the quadratic terms of the Hamiltonian of the restricted three body problem at a Lagrange equilateral triangle equilibrium point. 相似文献
11.
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
12.
13.
Tsutomu Takashima 《Astrophysics and Space Science》1975,36(2):319-328
The procedure of computing the intensity and the polarization parameters of radiation diffusely reflected and transmitted by an inhomogeneous, plane-parallel planetary atmosphere is discussed with the aid of the adding method. If the atmosphere is simulated by a number of homogeneous sublayers (aerosols and ozone may be included), the matrices of radiation diffusely reflected and transmitted by the atmosphere can be expressed in terms of these matrices of sublayers by using only a couple of iterative equations with the polarity effect of radiation. This procedure is to be extended to the model atmosphere bounded by the surface reflector with a quite arbitrary phase matrix. 相似文献
14.
The envelope of iso-energetic trajectories in the (repulsive) two-fixed-centre problem is derived. Our analytical calculations finally lead to a transcendental equation, only containing elliptic integrals and the Weierstraßp function, from which the envelope is constructed. The results may serve as a simple model for the boundary layer between two colliding supersonic stellar wind flows in binary systems, in which at least one of the components has a strong radiation field.Beyond this, the effect of non-inertial forces (centrifugal and Coriolis force) due to the binary's orbital motion has been estimated by a numerical analysis within the scope of the (repulsive) restricted three-body problem.All calculations have been performed for a hot model (Wolf-Rayet/O-star) binary system with a set of parameters which might be appropriate for HD 152270. The envelope may be well approximated by a hyperboloid. The non-inertial forces slightly turn the envelope against the line connecting both stars. 相似文献
15.
J. Dorschner 《Astronomische Nachrichten》1974,295(3):141-146
Basing on the author's work a review of the possibilities as well as the limits of treating the problem of the collisional history of the asteroids by analytical methods is given. Using empirical data on rock fragmentation and general principles like symmetry and mass conservation the distribution function of the fragments arising from a single collision is analytically formulated. The size distribution of asteroids adjusting when crushing collisions have taken place a sufficiently long time can be obtained as the solution of an integrodifferential equation with partial derivatives (equation of fragmentation). Quasi-stationary solutions of the equation of fragmentation are discussed for particular cases. The problem of the steady state is reduced to the solution of a transcendental equation. The results obtained show that analytical methods already offer a good theoretical understanding of the observed size distribution of the asteroids. They should be, therefore, a useful basis of carrying out numerical calculations. 相似文献
16.
This work studies a special type of cislunar periodic orbits in the circular restricted three-body problem called resonance transition periodic orbits, which switch between different resonances and revolve about the secondary with multiple loops during one period. In the practical computation, families of multiple periodic orbits are identified first, and then the invariant manifolds emanating from the unstable multiple periodic orbits are taken to generate resonant homoclinic connections, which are used to determine the initial guesses for computing the desired periodic orbits by means of multiple-shooting scheme. The obtained periodic orbits have potential applications for the missions requiring long-term continuous observation of the secondary and tour missions in a multi-body environment. 相似文献
17.
This paper investigates the equinoctial orbit elements for the two-body problem, showing that the associated matrices are free from singularities for zero eccentricities and zero and ninety degree inclinations. The matrix of the partial derivatives of the position and velocity vectors with respect to the orbit elements is given explicitly, together with the matrix of inverse partial derivatives, in order to facilitate construction of the matrizant (state transition matrix) corresponding to these elements. The Lagrange and Poisson bracket matrices are also given. The application of the equinoctial orbit elements to general and special perturbations is discussed.This work was initiated while the second author was a Postdoctoral Scholar in the School of Engineering and Applied Science, University of California, Los Angeles. 相似文献
18.
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
19.
Tomás Soler 《Celestial Mechanics and Dynamical Astronomy》1984,32(3):257-296
In this work a novel tensor-matrix notation is first introduced and later applied to develop a new general expression to compute the potential of a body at exterior points as a function of the full tensors of inertia. As a corollary the general matrix development of the gravitational attraction in function of the inertia tensors is also established. For clarity the first terms in both expansions are given explicitly in a simplified matrix form. Some classical particular cases still used in geophysical and geodetic literature are pointed out and discussed. 相似文献
20.
William B. Heard 《Astrophysics and Space Science》1976,43(1):63-82
The dynamics of an ensemble of particles emanating from a common point with a distribution of velocities is modeled as a continuum of particles described by a phase space distribution function. A general solution for the distribution function and the associated spatial density function is obtained for a general dynamical system. The special cases of linear dynamical systems and slow dispersion from a circular orbit are treated in detail. A transcendental equation is derived, the roots of which determine the time since initial dispersion from knowledge of the spatial density function at later times. 相似文献