共查询到20条相似文献，搜索用时 31 毫秒
1.
Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1978,18(2):195-204
It is shown that the appearance of higher order resonances (that produce higher order islands on a surface of section), is not an indication of non-integrability. Examples are given and a method is described for constructing integrable Hamiltonians with higher order resonances. 相似文献
2.
Expressions are given for the first order node-to-node perturbations in the orbital elements of a satellite due to an arbitrary zonal harmonic of the geopotential. Accurate and efficient procedures for computing such perturbations are necessary for orbit determination methods which will fully utilize the highly accurate observations now available.Comparison with a double precision numerical integration is made for an intermediate altitude satellite, TELSTAR I. (Second order perturbations due to the second harmonic, derived elsewhere, are included, as are the first order perturbations due to the zonals through fourteenth order.) Discrepancies in semi-major axis after 1 period are of the order of 0.1 mm. Discrepancies in timing are of the order of 0.03 msec. A detailed discussion of computational efficiency is included. 相似文献
3.
Yan Li 《Chinese Astronomy and Astrophysics》1989,13(4):424-431
A decoupling method is developed in this paper to deal with linear non-adiabatic non-radial pulsations of stars. The sixth order differential equation of linear pulsation is decomposed into a fourth order and a second order differential equations. The decoupling overcomes such difficulties encountered in the numerical solution as small domain and slowness of convergence and provides a natural guess solution needed in Henyey's method. 相似文献
4.
The nonlinear propagation of ion acoustic waves in ideal plasmas consisting of degenerate electrons and positrons, and isothermal ions is investigated. The Korteweg de Vries (K-dV) equation that contains the lowest order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (K-dV type) equation that accounts for the higher order nonlinearity and the dispersion relation is obtained. The stationary wave solution for these equations has been found using the renormalization method. Also, the effects of electrons and positrons densities and ion temperature on the amplitude and width of solitary waves are investigated, numerically. It is seen that higher order corrections significantly change the properties of the K-dV solitons. Also, it is found that both compressive and rarefactive solitary waves can be propagated in such plasma system. 相似文献
5.
Ch. Tsitouras 《Celestial Mechanics and Dynamical Astronomy》1999,74(4):223-230
A tenth order explicit symmetric and in consequence symplectic Runge–Kutta–Nyström method is presented here. We derive the order conditions needed and solve them for the parameters of the method. Numerical results indicate the superiority of the new method compared to the other high order symplectic methods appeared in the literature until now. 相似文献
6.
The motion around the libration points is studied with Charlier's first order theory assuming the isotropic mass variation of the primaries does not exceed the order of the small primary and the derivatives of the masses with respect to time are negligible second order quantities. The results are analogous to those obtained with constant primary masses. 相似文献
7.
The computation on a relatively short time of a quantity, related to the largest Lyapunov Characteristic Exponent, called Fast Lyapunov Indicator allows to discriminate between ordered and weak chaotic motion and also, under certain conditions, between resonant and non resonant regular orbits. The aim of this paper is to study numerically the relationship between the Fast Lyapunov Indicator values and the order of periodic orbits. Using the two-dimensional standard map as a model problem we have found that the Fast Lyapunov Indicator increases as the logarithm of the order of periodic orbits up to a given order. For higher order the Fast Lyapunov Indicator grows linearly with the order of the periodic orbits. We provide a simple model to explain the relationship that we have found between the values of the Fast Lyapunov Indicator, the order of the periodic orbits and also the minimum number of iterations needed to obtain the Fast Lyapunov Indicator values. 相似文献
8.
Mean orbital elements are obtained from osculating ones by removing the short periodic perturbations. Large catalogues of
asteroid mean elements need to be computed, as a first step in the computation of proper elements, used to study asteroid
families. The algorithms for this purpose available so far are only accurate to first order in the masses of the perturbing
planet; the mean elements have satisfactory accuracy for most of the asteroid belt, but degraded accuracy in the neighbourhoods
of the main mean motion resonances, especially the 2:1. We investigate a number of algorithms capable of improving this approximation;
they belong to the two classes of Breiter-type methods and iterative methods. The former are obtained by applying some higher
order numerical integration scheme, such as Runge–Kutta, to the differential equation whose solution is a transformation removing
the fast angular variables from the equations; they can be used to compute a full second order theory, however, only if the
full second order determining function is explicitly computed, and this is computationally too cumbersome for a complicated
problem such as the N-body. The latter are fixed point iterative schemes, with the first order theory as an iteration step,
used to compute the inverse map from mean to osculating elements; formally the method is first order, but because they implement
a fixed frequency perturbation theory, they are more accurate than conventional single iteration methods; a similar method
is already in use in our computation of proper from mean elements. Many of these methods are tested on a sample of asteroid
orbits taken from the Themis family, up to the edge of the 2:1 resonance, and the dispersion of the values of the computed
mean semimajor axis over 100 000 years is used as quality control. The results of these tests indicate that the iterative
methods are superior, in this specific application, to the Breiter methods, in accuracy and reliability. This is understood
as the result of the cancellations occurring between second order perturbation terms: the incomplete second order theory,
resulting from the use of a Breiter method with the first order determining function only, can be less accurate than complete,
fixed frequency theories of the first order. We have therefore computed new catalogues of asteroid mean and proper elements,
incorporating an iterative algorithm in both steps (osculating to mean and mean to proper elements). This new data set, significantly
more reliable even in the previously degraded regions of Themis and Cybele, is in the public domain.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
The non-linear stability of the triangular libration points of the restricted three-body problem is studied under the presence
of third and fourth order resonance's, when the more massive primary is an oblate spheroid. In this study Markeev's theorem
are utilised with the help of KAM theorem. It is found that the stability of the triangular libration points are unstable
in the third order resonance case and stable in the fourth order resonance case, for all the values of oblateness factor A1.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
10.
11.
S. V. Vorontsov 《Solar physics》1983,82(1-2):379-382
Perturbation theory is developed for calculating the influence of slow differential rotation on the adiabatic nonradial modes of stellar oscillations. The effects of Coriolis forces and ellipticity are analysed simultaneously using the perturbation technique for Hermitian operators which is developed up to second order in eigenvalues and to first order in eigenvectors. 相似文献
12.
The first order (in the massm of the central body) time delay is deduced for all theories of gravitation that satisfy the 3-dimensional principle of equivalence in the one-body problem. It is shown that the curvature of the light ray causes no first order time delay but that the first order time delay is sensitive to the non-linear term of a general metric when distancesr are measured by the periods of circular planetary orbits. 相似文献
13.
Eric Bois 《Celestial Mechanics and Dynamical Astronomy》1987,42(1-4):141-168
This work presents the expansion of the second-order of an analytical theory of the attitude evolution of an artificial satellite perturbed by given torques. The first-order of the theory has already been presented by the author in Celestial Mechanics39 (1986) 309–327. It is a theory that is valid under very general conditions including slow rotation and inequal axes of inertia. The present theory is suitable for any internal or external disturbing forces producing the torques. A formal solution is expanded in the second-order according to powers of a small parameter characteristic of the order of magnitude of the disturbing torques. These torques are expanded in Fourier series and the theory applies whatever is the length of these series. The coefficients of the solution are given by an iterative formation law. The comparison of the results with a numerical integration based upon a HIPPARCOS model shows that the second order has brought an improvement to the theory by at least one order of magnitude over the results of the first order. 相似文献
14.
Demetrius A. Vaiopoulos 《Astrophysics and Space Science》1980,71(1):239-247
It is known that a special case of the Lagrangian of two identical charged particles up to fourth order terms has been found. The object of this paper is to derive the generalized Lagrangian by a scheme which is somewhat different from the one known. On the other hand one can then proceed to give the Hamiltonian form up to the same order. 相似文献
15.
We study the periodic motion around the collinear equilibrium points of the restricted three-body problem when the primary is a source of radiation and the secondary is an oblate spheroid. In particular, the Liapunov families of two and three dimensional periodic orbits are computed. In order to gain the appropriate initial conditions a third-fourth order Lindstedt-Poincaré local analysis is used. The stability of these families is also computed. 相似文献
16.
Deprit and Miller have conjectured that normalization of integrable Hamiltonians may produce normal forms exhibiting degenerate equilibria to very high order. Several examples in the class of coupled elliptic oscillators are known. In order to test the utility of normalization as a detector of integrability we normalize, to high order, a perturbed Keplerian system known to have several integrable limits; the generalized van der Waals Hamiltonian for a hydrogen atom. While the separable limits give rise to high order degeneracy we find a non-separable, integrable limit for which the normal form does not exhibit degeneracy. We conclude that normalization may, in certain cases, indicate integrability but is not guaranteed to uncover all integrable limits. 相似文献
17.
Liam M. Healy 《Celestial Mechanics and Dynamical Astronomy》2000,76(2):79-120
Using the elimination of the parallax followed by the Delaunay normalization, we present a procedure for calculating a normal
form of the main problem (J
2 perturbation only) in satellite theory. This procedure is outlined in such a way that an object-oriented automatic symbolic
manipulator based on a hierarchy of algebras can perform this computation. The Hamiltonian after the Delaunay normalization
is presented to order six explicitly in closed form, that is, in which there is no expansion in the eccentricity. The corresponding
generating function and transformation of coordinates, too lengthy to present here to the same order; the generator is given
through order four.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
18.
李焱 《中国天文和天体物理学报》1989,(4)
本文发展了一种解恒星线性非绝热非径向脉动问题的退耦化方法。这个方法把非绝热非径向脉动问题的六阶线性微分方程,分解为由一个代数方程联系起来的一个四阶线性微分方程和另一个二阶线性微分方程进行数值求解。这样的一个退耦处理,有利于克服以前在数值解这类问题时常常遇到的收敛域小和收敛速度慢等困难,并且为数值解方程时所采用的Henyey方法提供了一个自然和方便的初始猜测解。 相似文献
19.
Vittorio Banfi 《Earth, Moon, and Planets》1991,54(3):269-282
A theoretical model, based on particular type of the restricted three-body problem, is here presented in order to demonstrate the existence of a possible planetary motion near the center of mass in a binary star system. The superposition principle is used, with the introduction of two fictitious negative masses in order to simulate the real two primary bodies system. 相似文献
20.
W.B. Hubbard 《Icarus》1976,27(3):387-389
We evaluate the departures from Bouguer's law for the case of an oblate atmosphere. We show that, to lowest order, the plane of refraction is defined by the normal to the atmosphere at closest approach. In next order, however, the ray path is “warped” by the oblateness, which changes slightly the plane of refraction. 相似文献