共查询到20条相似文献，搜索用时 15 毫秒
1.
Osman M. Kamel 《Earth, Moon, and Planets》1989,47(1):73-89
The construction of a third order J-S theory is presented. The Hori theory of planetary perturbations is employed. No Critical J-S terms due to the 2:5 commensurabilities and its multiples exist, when we take into account the periodic terms of order 0, 1, 2 with respect to the eccentricity- inclination. In this case the Lie series transformation degenerates and is meaningless. The J-S equations of motion for secular perturbations are solved when we neglect in our treatment, the Poisson terms of degree > 2 in the Poincaré canonical variables H
u
, K
u
, P
u
Q
u
(u = 1, 2). The Jacobi-Radau referential is adopted, and the theory is expressed in terms of the canonical variables of H. Poincaré.Now at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, U.S.A. 相似文献
2.
Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):305-328
As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete
elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9–19 obtained by truncating Taylor series
expansions of the integrals. Otherwise, the associate integrals, K(1 − m) and E(1 − m), are first computed by a pair of the approximate polynomials and then transformed to K(m) and E(m) by means of Jacobi’s nome, q, and Legendre’s identity relation. In average, the new method runs more-than-twice faster than the existing methods including
Cody’s Chebyshev polynomial approximation of Hastings type and Innes’ formulation based on q-series expansions. Next, we invented a fast procedure to compute simultaneously three Jacobian elliptic functions, sn(u|m), cn(u|m), and dn(u|m), by repeated usage of the double argument formulae starting from the Maclaurin series expansions with respect to the elliptic
argument, u, after its domain is reduced to the standard range, 0 ≤ u < K(m)/4, with the help of the new method to compute K(m). The new procedure is 25–70% faster than the methods based on the Gauss transformation such as Bulirsch’s algorithm, sncndn, quoted in the Numerical Recipes even if the acceleration of computation of K(m) is not taken into account. 相似文献
3.
Osman M. Kamel 《Earth, Moon, and Planets》1996,74(1):1-6
We present a literal approach to evaluate –s
necessary for the construction of high order planetary theories. This approach is valid to be applied on very large scale digital computers with standard Poisson series programs, for high order and high degree planetary theories. We apply the method of symbolic differential operators for single variable functions, and the binomial theorem expansions, for the evaluation of –s
. We utilize Laplace coefficients and its derivatives to carry out the development, without dealing with Newcomb operators or Hansen's coefficients. 相似文献
4.
This is the second paper in a series of articles devoted to one of the basic problems of celestial mechanics: the evolution of solar-type planetary systems. In the first paper (Kholshevnikov et al., 2001), we reviewed the history and the current state of the issue, outlined the scheme of the study, introduced Jacobi coordinates and related osculating elements, and indicated the form of the Hamiltonian expansion into a Poisson series in all elements. In this paper, the expansion coefficients are found according to a simple algorithm that is reduced to the calculation of multiple integrals of elementary functions. At the first stage, we restricted our analysis to the two-planetary problem (Sun–Jupiter–Saturn). The general case will be investigated in a forthcoming paper. 相似文献
5.
Marcel O. Vlad 《Astrophysics and Space Science》1994,218(2):159-174
The stochastic gravitational fluctuations for a fractal mass distribution are analyzed by means of a functional integral approach. A general method is developed for evaluating the stochastic properties of vectorial additive random fields generated by a variable number of point sources obeying inhomogeneous Poisson statistics. A closed expression for the generating functional of the field is given in terms of the generating functional of the sources. The moments of the resulting vectorial field are finite if the correlation functions of the sources have short tails. In this case all cumulants of the field can be computed exactly: they are averages of the central moments of sources computed in terms of the probability density of the position of a source. The method is applied for analyzing the stochastic gravitational fluctuations generated by a fractal distribution of field sources (stars or galaxies). For a Newtonian force law the correlation functions of the sources are slowly decaying, the cumulants of the stochastic gravitational field are infinite and the probability density of the field intensityF is given by a Lévy fractal stable law with a scaling exponentH depending on the fractal dimensiond
f
of the distribution of stars or galaxies:H =d
f
/2. 相似文献
6.
É. Kh. Danielyan 《Astrophysics》1994,37(1):79-88
Analytical investigations of the method of linear nonsingular integral equations, originally proposed by É. Kh. Danielyan [Astrofizika
36,225 (1993)] for the solution of problems in the theory of radiative transport in a medium of finite optical thickness with isotropic scattering, are continued in the present article. It is shown that the solution of problems of the stated class reduce to the determination of only the functions u
±
(, ) in the general case with true absorption. Explicit expressions are obtained for these functions at =0. The feasibility of a complete analytical solution of the problem is newly formulated as the solution of a Fredholm integral equation on the semiaxis with a kernel that admits representation by a superposition of exponential functions [Eq. (25)]. The choice of an efficient procedure for determining the Ambartsumyan -function for a semiinfinite medium is discussed. In particular, a new equation is given for this function.Translated from Astrofizika, Vol. 37, No. 1, pp. 129–145, January–March, 1994. 相似文献
7.
R. A. Krikorian 《Astrophysics》1999,42(3):338-343
The field-to-particle method of H. P. Robertson as applied by Noonan, in order to obtain the general relativistic equations
describing the trajectory of a photon in a refractive medium, is compared with Synge’s general relativistic Hamiltonian theory
of waves and rays. For a photon in vacuum it is known that both approaches yield the same equation for the trajectory, i.e.,
a null geodesic. However for a photon in a medium, in contradistinction to the Hamiltonian theory, the field-to-particle method
(a) yields equations of the photon trajectory valid only in a nondispersive medium, (b) the time component u0
of the tangent to the ray remains an undetermined quantity, (c) agreement with the Hamiltonian theory is achieved by substituting
into Noonan’s equations the Hamiltonian expression for u
0.
Published in Astrofizika, Vol. 42, No. 3, pp. 449–455, July–September, 1999. 相似文献
8.
M. Clutton-Brock 《Astrophysics and Space Science》1972,19(1):225-247
The aim of this series of papers is to develop straightforward methods of computing the response of flat galaxies to small perturbations. This Paper I considers steady state problems; Paper II considers time varying perturbations and the effects of resonances; and Paper III applies the methods developed in Papers I and II to a numerical study of the stability of flat galaxies.The general approach is to study the dynamics of each individual orbit. The orbits are described by their apocentric and pericentric radii,r
a
andr
p
, and the distribution function of an equilibrium model is a function ofr
a
andr
p
. The mass density and potential corresponding to a distribution function is found by means of an expansion in Hankel-Laguerre functions; the coefficients of the expansion being found by taking moments of the mass density of the individual orbits. This leads to a simple method of constructing equilibrium models.The response to a small perturbation is found by seeking the response of each orbit. When the perturbations are axisymmetric and slowly varying, the response can be easily found using adiabatic invariants. The potential is expanded in a series of Hankel-Laguerre functions, and the response operator becomes a discrete matrix. The condition that the model is stable against adiabatic radial perturbations is that the largest eigenvalue of the response matrix should be less than one.An analytic approximation to the response matrix is derived, and applied to estimate the eccentricity needed for stability against local perturbations. 相似文献
9.
Ray G. Langebartel 《Astrophysics and Space Science》1979,60(2):431-439
The Laplace equation in the coordinatesu, v, w is calledu-separable if there are solutions of the formF(u)G(v, w). If the surfacesv = constant andw = constant are orthogonal tou = constant the coordinate system is called semi-orthogonal. The Laplace equation is notu-separable for the rotation problem semi-orthogonal Roche coordinate system (n0, q=0) or the general problem (n0, q0) ifv andw are analytic functions ofn andq and the coordinate system is proper in some region of then, q plane including the origin,n=q=0 (u is the Roche potential). 相似文献
10.
R. Tschaepe 《Astrophysics and Space Science》1987,129(1):149-158
Numerical computation of the gravitational potential for arbitrary mass distribution in spherical coordinates is considered. It is possible to determine the potential from the spherical expansion of the Poisson integral with 1/2n
2
NML operations — i.e., with a number proportional to the mesh numberNML multiplied by the square of the Legendre functions of indexn. The computation of the potential based on the solution of the Poisson differential equation is discussed. 相似文献
11.
Yūki Kubo 《Solar physics》2008,248(1):85-98
This article discusses statistical models for the solar flare interval distribution in individual active regions. We analyzed
solar flare data in 55 active regions that are listed in the Geosynchronous Operational Environmental Satellite (GOES) soft X-ray flare catalog for the years from 1981 to 2005. We discuss some problems with a conventional procedure to
derive probability density functions from any data set and propose a new procedure, which uses the maximum likelihood method
and Akaike Information Criterion (AIC) to objectively compare some competing probability density functions. Previous studies
of the solar flare interval distribution in individual active regions only dealt with constant or time-dependent Poisson process
models, and no other models were discussed. We examine three models – exponential, lognormal, and inverse Gaussian – as competing
models for probability density functions in this study. We found that lognormal and inverse Gaussian models are more likely
models than the exponential model for the solar flare interval distribution in individual active regions. The possible solar
flare mechanisms for the distribution models are briefly mentioned. We also briefly investigated the time dependence of probability
density functions of the solar flare interval distribution and found that some active regions show time dependence for lognormal
and inverse Gaussian distribution functions. The results suggest that solar flares do not occur randomly in time; rather,
solar flare intervals appear to be regulated by solar flare mechanisms. Determining a solar flare interval distribution is
an essential step in probabilistic solar flare forecasting methods in space weather research. We briefly mention a probabilistic
solar flare forecasting method as an application of a solar flare interval distribution analysis. The application of our distribution
analysis to a probabilistic solar flare forecasting method is one of the main objectives of this study. 相似文献
12.
We propose the Ptolemaic transformation: a canonical change of variables reducing the Keplerian motion to the form of a perturbed Hamiltonian problem. As a solution of the unperturbed case, the Ptolemaic variables define an intermediary orbit, accurate up to the first power of eccentricity, like in the kinematic model of Claudius Ptolemy. In order to normalize the perturbed Hamiltonian we modify the recurrent Lie series algorithm of HoriuuMersman. The modified algorithm accounts for the loss of a term's order during the evaluation of a Poisson bracket, and thus can be also applied in resonance problems. The normalized Hamiltonian consists of a single Keplerian term; the mean Ptolemaic variables occur to be trivial, linear functions of the Delaunay actions and angles. The generator of the transformation may serve to expand various functions in Poisson series of eccentricity and mean anomaly. 相似文献
13.
E. Kh. Danielian 《Astrophysics》2011,54(2):250-268
New methods are proposed for finding the Ambartsumyan functions φ(η) for a half space and φ(η, τ) and ψ(η, τ) for finite layers,
as well as their analogs with complete frequency redistribution, X (z, τ) and Y (z, τ). Substantial simplifications are obtained for monochromatic conservative scattering. Besides the Ambartsumyan functions,
expressions for several of their angular moments are obtained directly in terms of the basis functions u
±. A system of differential equations is obtained for the basis functions. A system of equations without the characteristic
pseudosingularities is obtained for φ(η, τ) and ψ(η, τ) instead of the classical system of nonlinear equations. Some aspects
of the numerical realization of the proposed method are also discussed. 相似文献
14.
This paper is the third in a series of articles devoted to one of the basic problems of celestial mechanics: the study of the evolution of solar-type planetary systems. In the previous papers a brief review of the history and current state of the problem was given; the plan of the study was outlined; the Jacobi coordinates and the related osculating elements were introduced; the form of the Poisson expansion of the Hamiltonian in all elements was given; and the expansion coefficients for the Hamiltonian of the two-planetary Sun–Jupiter–Saturn problem were obtained (though with impure accuracy) by a simple algorithm that is reduced to the calculation of multiple integrals of elementary functions. In the present paper the expansion of the Hamiltonian of the two-planetary Sun–Jupiter–Saturn problem into the Poisson series in all elements is constructed with the help of the PSP Poisson series processor, which is capable of required accuracy. 相似文献
15.
N. X. Vinh 《Celestial Mechanics and Dynamical Astronomy》1970,2(1):64-76
In this paper we derive some recurrence formulae which can be used to calculate the Fourier expansions of the functions (r/a)
n
cosmv and (r/a)
n
sinmv in terms of the eccentric anomalyE or the mean anomalyM. We also establish a recurrence process for computing the series expansions for alln andm when the expansions of two basic series are known. These basic series were given in explicit form in the classical literature. The recurrence formulae are linear in the functions involved and thus make very simple the computation of the series.This work was supported by NASA contract No. NASr 54(06).—The paper was presented at the AIAA/AAS meeting, Princeton University, August 1969. 相似文献
16.
A. G. Nikoghossian 《Astrophysics》2004,47(1):104-116
This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres. 相似文献
17.
In this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the massM u of an infinitely extended, homogeneously matter‐filled and expanding universe. To answer this question we produce a space‐like sum of instantaneous cosmic energy depositions surrounding equally each spacepoint in the homogeneous universe. We calculate the added‐up instantaneous cosmic energy per volume around an arbitrary space point in the expanding universe. To carry out this sum we use as basic metrics an analogy to the inner Schwarzschild metric applied to stars, but this time applied to the spacepoint‐related universe. It is then shown that this leads to the added‐up proper energy within a sphere of a finite outer critical radius defining the point‐related infinity. As a surprise this radius turns out to be reciprocal to the square root of the prevailing average cosmic energy density. The equivalent mass of the universe can then also be calculated and, by the expression which is obtained here, shows a scaling with this critical radius of this universe, a virtue of the universe which was already often called for in earlier works by E. Mach, H. Thirring and F. Hoyle and others. This radius on the other hand can be shown to be nearly equal to the Schwarzschild radius of the so‐defined mass M u of the universe. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
S. I. Grachev 《Astrophysics》2001,44(4):505-517
A new method is proposed for the numerical solution of nonsteady problems in the theory of radiative transfer. In this method, if the solution at some time t (such as the initial time) is known, then by representing the radiation intensity and all time-dependent quantities (level populations, kinetic temperature, etc.) in the form of Taylor series expansions in the vicinity of t, one can, from the transfer equation and the equations accompanying it (population equations, energy-balance equation, etc.), find all derivatives of that solution at the given time from certain recursive equations. From the Taylor series one can then calculate the solution at some later time t + t, and so forth. The method enables one to analyze nonsteady tradiative transfer both in stationary media and in media with characteristics that vary with time in a given way. This method can also be used to solve nonlinear problems, i.e., those in which the radiation field significantly affects the characteristics of the medium. No iterations are used for this: everything comes down to calculations based on recursive equations. Several problems, both linear and nonlinear, are solved as examples. 相似文献
19.
The diffusion of scalar fields (temperature, density number of some admixture) in a compressible medium showing an isotropic, homogeneous and stationary turbulence is considered. The derived formulae for turbulent diffusivity χT(ξ) hold up to ξ ≈ 1, where ξ = u0 τ0/R0 (u0, τ0, and R0 are characteristic velocity, life-time, and correlation length of turbulent pulsations, respectively. The velocity field of turbulent motions u(r, t) is assumed to be known and the influence of the scalar field onto u(r, t) is neglected. It is shown that the velocity correlators, which change their signs in dependence on the space corrdinates, may give negative values for ξT(ξ) when ξ ≠ 0. 相似文献
20.
《New Astronomy》2017
We introduce the method of multiple cross-wavelet algorithm, hereafter also as Einstein’s cross functions, for the time-frequency study of solar activity records or any astronomical and geophysical time series in general. The main purpose of this algorithm is to allow the simultaneous examination of the time-frequency information contents in n > 2 time series available. Previous cross-wavelet algorithm only permit the study of two time series at a time and was not extended to the generalized n > 2 problems until now. Furthermore, our new work lifted the restriction from the original formulation that are valid only for stationary processes. We applied our new algorithm to several of the solar activity proxies available in order to demonstrate the broad and powerful utility of this technique. We have used solar activity proxy records that are obtained under different geophysical archives and time periods which are, in turn, suitable for studying both the statistical and physical properties for solar variations valid on timescales of multi-century, millennium to several millennia. We focus on documenting the methodology in this paper rather than any elaborate interpretation of the results. 相似文献