共查询到20条相似文献，搜索用时 316 毫秒
1.
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
2.
Mervat El-Sayed Awad 《Earth, Moon, and Planets》1995,69(1):1-12
In this paper an analytical solution for the differential equations governing the motion of Artificial Satellite under the oblateness of the earth will be developed. We start with the differential equations in terms of Euler parameters. To compact algebra, we introduce the Cayley-Klein type complex variables. Comparison between numerical and analytical final states withJ
2 will be given for a test case. 相似文献
3.
Haruo Yoshida 《Celestial Mechanics and Dynamical Astronomy》1992,53(2):145-150
A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively. 相似文献
4.
B. P. Kondratyev 《Solar System Research》2011,45(1):60-74
A flexible and informative vector approach to the problem of physical libration of the rigid Moon has been developed in which
three Euler differential equations are supplemented by 12 kinematic ones. A linearized system of equations can be split into
an even and odd systems with respect to the reflection in the plane of the lunar equator, and rotational oscillations of the
Moon are presented by superposition of librations in longitude and latitude. The former is described by three equations and
consists of unrestricted oscillations with a period of T
1 = 2.878 Julian years (amplitude of 1.855″) and forced oscillations with periods of T
2 = 27.201 days (15.304″), one stellar year (0.008″), half a year (0.115″), and the third of a year (0.0003″) (five harmonics
altogether). A zero frequency solution has also been obtained. The effect of the Sun on these oscillations is two orders of
magnitude less than that of the Earth. The libration in latitude is presented by five equations and, at pertrubations from
the Earth, is described by two harmonics of unrestricted oscillations (T
5 ≈ 74.180 Julian years, T
6 ≈ 27.347 days) and one harmonic of forced oscillations (T
3 = 27.212 days). The motion of the true pole is presented by the same harmonics, with the maximum deviation from the Cassini
pole being 45.3″. The fifth (zero) frequency yields a stationary solution with a conic precession of the rotation axis (previously
unknown). The third Cassini law has been proved. The amplitudes of unrestricted oscillations have been determined from comparison
with observations. For the ratio $
\frac{{\sin I}}
{{\sin \left( {I + i} \right)}} \approx 0.2311
$
\frac{{\sin I}}
{{\sin \left( {I + i} \right)}} \approx 0.2311
, the theory gives 0.2319, which confirms the adequacy of the approach. Some statements of the previous theory are revised.
Poinsot’s method is shown to be irrelevant in describing librations of the Moon. The Moon does not have free (Euler) oscillations;
it has oscillations with a period of T
5 ≈ 74.180 Julian years rather than T ≈ 148.167 Julian years. 相似文献
5.
Theory of the motion of an artificial Earth satellite 总被引：1，自引：0，他引：1
Felix R. Hoots 《Celestial Mechanics and Dynamical Astronomy》1981,23(4):307-363
An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ
4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order.Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions. 相似文献
6.
M. A. Vashkov’yak 《Solar System Research》2010,44(6):527-540
A new analytical solution of the system of differential equations describing secular perturbations and long-period solar perturbations
of mean orbits of outer satellites of giant planets was obtained. As distinct from other solutions, the solution constructed
using von Zeipel’s method approximately takes into account, in the secular part of the perturbing function, the totality of
fourth order with respect to the small parameter m of the ratio of the mean motions of the primary planet and the satellite. This enables us to describe more accurately the
evolution of satellite orbits with large apocentric distances, which in the course of evolution may exceed the halved radius
of the Hill sphere of the planet with respect to the Sun. Among these are the orbits of the two outermost Neptunian satellites
N10 (Psamathe) and N13 (Neso). For these satellites, the parameter m amounts to 0.152 and 0.165, respectively. Different from a purely analytical solution, the proposed solution requires preliminary
calculations for each satellite. More precisely, in doing so, we need to construct some simple functions to approximate more
complex ones. This is why we use the phrase “constructive analytical.” To illustrate the solution, we compare it with the
results of the numerical integration of the strict motion equations of the satellites N10 and N13 over time intervals 5–15
thousand years. 相似文献
7.
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
8.
Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary
problems. Their solution via differential equations implies making hypotheses on the solution itself, namely the specific
intensity I (τ; n) of the radiation field. On the contrary, integral methods require making hypotheses on the source function S(τ). It seems of course more reasonable to make hypotheses on the latter because one can expect that the run of S(τ) with depth is smoother than that of I (τ; n). In previous works we assumed a piecewise parabolic approximation for the source function, which warrants the continuity
of S(τ) and its first derivative at each depth point. Here we impose the continuity of the second derivative S′′(τ). In other words, we adopt a cubic spline representation to the source function, which highly stabilizes the numerical
processes. 相似文献
9.
Chris Koen 《Astrophysics and Space Science》1987,136(1):91-99
A technique for finding the oscillation spectrum of a rotating star based on the solution of two simultaneous ordinary differential equations is described. Results are presented for someg-modes of the polytrope of index 2. It appears that the functional dependence of frequency on rotational velocity is different for different azimuthal wave numbersm. 相似文献
10.
The numerical integration of the differential equations describing dynamical systems has been shown in previous papers of this series to be most effectively accomplished by an explicit Taylor series method.In this paper we show that one explicit Taylor series method, developed earlier in this series and which appears to possess a high degree of versatility, yields considerable gains in efficiency over classical single-step and multi-step methods. (In this context efficiency is a measure of the time taken to carry out a calculation of a specific accuracy).For a given accuracy criterion governing the local truncation error (LTE) it is found that the Taylor series method is generallytwice as fast as the classical multi-step method and up totwenty times faster than the classical single-step method. 相似文献
11.
We study the Brans-Dicke vacuum field equations in the presence of a cosmological term A. Considering a Friedmann-Robertson-Walker metric with flat spatial sections (k=0), we provide a qualitative analysis of the solutions and investigate its asymptotic properties. The general solution of the field equations for arbitrary values ofw and A is obtained.Work supported by CNPq (Brazil). 相似文献
12.
A necessary and a sufficient condition are derived for the ideal magnetohydrodynamic stability of any 3D magnetohydrostatic equilibrium using the energy method and incorporating photospheric line-tying. The theory is demonstrated by application to a simple class of theoretical 3D equilibria. The main thrust of the method is the formulation of the stability conditions as two sets of ordinary differential equations together with appropriate boundary conditions which may be numerically integrated along tied field lines one at a time. In the case of the shearless fields with non-negligible plasma pressure treated here the conditions for stability arenecessary and sufficient. The method employs as a trial function a destabilizing ballooning mode, of large wave number vector perpendicular to the equilibrium field lines. These modes may not be picked up in a solution of the full partial differential equations which arise from a direct treatment of the problem. 相似文献
13.
The orbit-averaged differential equations of motion of dust particles under gravity, radiation pressure and Poynting-Robertson drag were given by Wyatt and Whipple (1950). An integral of motion enables the system of two equations in semi-major axis a and eccentricity e to be reduced to one equation, the solution of which is presented here in terms of analytical formulae. An efficient numerical algorithm to compute the solution is given. Listings of two FORTRAN routines are included. 相似文献
14.
The solution curves of the differential equations determining the behavior of the solar wind are calculated for the case where the heat flux has its maximum value 3/2 nkTv
th. All the supersonic solutions are asymptotically adiabatic, T r
-4/3.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
15.
The Integral Variation (IV) method is a technique to generate an approximate solution to initial value problems involving systems of first-order ordinary differential equations. The technique makes use of generalized Fourier expansions in terms of shifted orthogonal polynomials. The IV method is briefly described and then applied to the problem of near Earth satellite orbit prediction. In particular, we will solve the Lagrange planetary equations including the first three zonal harmonics and drag. This is a highly nonlinear system of six coupled first-order differential equations. Comparison with direct numerical integration shows that the IV method indeed provides accurate analytical approximations to the orbit prediction problem.Advanced Systems Studies; Bldg. 254EElectro-Optical Systems Laboratory; Bldg. 201. 相似文献
16.
Ghodrat Ebadi Aida Mojaver Daniela Milovic Stephen Johnson Anjan Biswas 《Astrophysics and Space Science》2012,341(2):507-513
In this paper, we present G′/G-expansion method, exp-function method, modified F-expansion method as well as the traveling wave hypothesis for finding the exact traveling wave solutions of the quantum Zakharov-Kuznetsov equation which arises in quantum magneto-plasmas. By these methods, rich families of exact solutions have been obtained, including soliton solutions. This work continues to reinforce the idea that the proposed methods, with the help of symbolic computation, provide a powerful mathematical tool for solving nonlinear partial differential equations. 相似文献
17.
Under the assumption of a power law (k·R
n=C,C=const.) between the gravitational constantk and the radius of curvatureR of the Universe and forP=1/3 the exact solution is sought for the cosmological equations of Brans and Dicke. The solution turns out to be valid for closed space and the parameter of the scalar-tensor theory is necessarily negative. The radius of curvature increases linearly with respect to the age of the Universe while the gravitational constant grows with the square of the radius of curvature. It has been shown (Lessner, 1974) that in this case (KR
2) the spatial component of the field equations is independent of the remaining equations. However, our solution satisfies this independent equation. This solution for the radiation-dominated era corresponds to the solution for the matter-dominated era found by Dehnen and one of the authors (Dehnen and Obregón, 1971). Our solution, as is the solution previously obtained for the matter-dominated era, is in contradiction to Dirac's hypothesis in which the gravitational constant should decrease with time in an expanding Universe. 相似文献
18.
G. A. Krasinsky 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):169-217
Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. The equations describe both the precession-nutational motion and the axial rotation (i.e. variations of the Universal Time UT). Poincaré’s method of modeling the dynamical effects of the fluid core, and Sasao’s approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. Some important perturbations ignored in the currently adopted theory of the Earth’s rotation are considered. In particular, these are the perturbing torques induced by redistribution of the density within the Earth due to the tidal deformations of the Earth and its core (including the effects of the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted for in the adopted Nutation IAU 2000, in which the tidal variations of the moments of inertia of the mantle and core are the only body tide effects taken into consideration. The equations explicitly depend on the three tidal phase lags δ, δ
c, δ
i responsible for dissipation of energy in the Earth as a whole, and in its external and inner cores, respectively. Apart from the tidal effects, the differential equations account for the non-tidal interaction between the mantle and external core near their boundary. The equations are presented in a simple close form suitable for numerical integration. Such integration has been carried out with subsequent fitting the constructed numerical theory to the VLBI-based Celestial Pole positions and variations of UT for the time span 1984–2005. Details of the fitting are given in the second part of this work presented as a separate paper (Krasinsky and Vasilyev 2006) hereafter referred to as Paper 2. The resulting Weighted Root Mean Square (WRMS) errors of the residuals dθ, sin θd for the angles of nutation θ and precession are 0.136 mas and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for IAU 2000 theory. The WRMS error of the UT residuals is 18 ms. 相似文献
19.
Aimed at the initial value problem of the particular second-order ordinary differential equations,y
=f(x, y), the symmetric methods (Quinlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have been compared in detail by integrating the artificial earth satellite orbits in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order formula of the symmetric methods when the integration time-interval is not greater than 12000 periods. 相似文献
20.
The problem of the detailed structure of magnetogasdynamic shock waves is investigated. It is assumed that the flow takes place under normal magnetic fieldH
0 and the conductivity of the medium is considered infinite. An approximate analytical solution of the nonlinear differential equations describing the phenomena is obtained. The suggested analytical results in this paper are in good agreement with the previous numerical computations for the thickness and the velocity distribution inside the transition region. In addition, the enthalpy distribution inside the shock front is predicted. 相似文献