共查询到20条相似文献，搜索用时 15 毫秒
1.
In a paper by the second author (Nacozy, 1981), various time elements are presented for use with the Sundman time transformation. In that paper, the time elements are given in terms of Keplerianorbital elements. We give here the corresponding time elements in terms ofrectangular coordinates. Extensive references are given in the previous paper and will be omitted here.We present additional numerical experiments comparing the use of time elementsand time transformationstogether with the use of time transformationsalone. The results indicate a reduction in computational error when time elements are used. 相似文献
2.
Paul Nacozy 《Celestial Mechanics and Dynamical Astronomy》1976,13(4):495-501
A review and discussion of several investigations concerning the effect of time transformations on numerical integration errors is given. In particular, the discussion treats the relation between time transformations andlocal truncation errors. Additional numerical results are presented which indicate that time transformations reducelocal truncation errors. The results complement those of other studies, especially the recent studies of Danby, Wong, Velez, and Feagin and Mikkilineni. A Sundman time transformation with avarying exponent is introduced and discussed. 相似文献
3.
We consider Sundman and Poincaré transformations for the long-time numerical integration of Hamiltonian systems whose evolution occurs at different time scales. The transformed systems are numerically integrated using explicit symplectic methods. The schemes we consider are explicit symplectic methods with adaptive time steps and they generalise other methods from the literature, while exhibiting a high performance. The Sundman transformation can also be used on non-Hamiltonian systems while the Poincaré transformation can be used, in some cases, with more efficient symplectic integrators. The performance of both transformations with different symplectic methods is analysed on several numerical examples. 相似文献
4.
Victor R. Bond 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):333-311
A new set of element differential equations for the perturbed two-body motion is derived. The elements are canonical and are similar to the classical canonical Poincaré elements, which have time as the independent variable. The phase space is extended by introducing the total energy and time as canonically conjugated variables. The new independent variable is, to within an additive constant, the eccentric anomaly. These elements are compared to the Kustaanheimo-Stiefel (KS) element differential equations, which also have the eccentric anomaly as the independent variable. For several numerical examples, the accuracy and stability of the new set are equal to those of the KS solution. This comparable accuracy result can probably be attributed to the fact that both sets have the same time element and very similar energy elements. The new set has only 8 elements, compared to 10 elements for the KS set. Both sets are free from singularities due to vanishing eccentricity and inclination. 相似文献
5.
Victor R. Bond 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):333
A new set of element differential equations for the perturbed two-body motions is derived. The elements are canonical and are similar to the classical canonical Poincaré elements, which have time as the independent variable. The phase space is extended by introducing the total energy and time as canonically conjugated variables. The new independent variable is, to within an additive constant, the eccentric anomaly. These elements are compared to the Kustaanheimo-Stiefel (KS) element differential equations, which also have the eccentric anomaly as the independent variable. For several numerical examples, the accuracy and stability of the new set are equal to those of the KS solution. This comparable accuracy result can probably be attributed to the fact that both sets have the same time element and very similar energy elements. The new set has only 8 elements, compared to 10 elements for the KS set. Both sets are free from singularities due to vanishing eccentricity and inclination.This paper is published in its entirety inCelest. Mech.
13 (1976), 287–311. 相似文献
6.
Mohammed Adel Sharaf Mervat El-Sayed Awad Samiha Al-Sayed Abdullah Najmuldeen 《Earth, Moon, and Planets》1992,56(2):141-164
In this paper, the classical and generalized Sundman time transformations are used to establish new generating set of differential equations of motion in terms of the Eulerian redundant parameters. The implementation of this set on digital computers for the commonly used independent variables is developed once and for all. Motion prediction algorithms based on these equations are developed in a recursive manner for the motions in the Earth's gravitational field with axial symmetry whatever the number of the zonal harmonic terms may be. Applications for the two types of short and long term predictions are considered for the perturbed motion in the Earth's gravitational field with axial symmetry with zonal harmonic terms up to J
36
. Numerical results proved the very high efficiency and flexibility of the developed equations. 相似文献
7.
Paul Nacozy 《Celestial Mechanics and Dynamical Astronomy》1976,14(1):129-132
Numerical results have shown that the use of time elements with time transformations provides increased accuracy in the numerical solution of gravitational systems.To gain additional accuracy improvements, it appears that the time and the time element should be calculated from quantities that have been adjusted so as to satisfy the energy integral exactly.We also have found that by reducing the growth of the time element to being nearly linear rather than quadratic causes an increase in the magnitude of the local truncation error in the solution but with a decrease in the rate of growth of the truncation error. 相似文献
8.
Ram Krishan Sharma 《Celestial Mechanics and Dynamical Astronomy》1989,46(4):321-333
Analytical solutions using KS elements are derived. The perturbation considered is the Earth's zonal harmonic J
2. The series expansions include terms of fourth power in the eccentricity. Only two of the nine KS element equations are integrated analytically due to the reasons of symmetry. The analytical solution is suitable for short-term orbit computations. Numerical studies show that reasonably good estimates of the orbital elements can be obtained in one step of 10 to 30 degrees of eccentric anomaly for near-Earth orbits of moderate eccentricity. For application purposes, the analytical solution can be effectively used for onboard computation in the navigation and guidance packages, where the modelling of J
2 effect becomes necessary. 相似文献
9.
G. Scheifele 《Celestial Mechanics and Dynamical Astronomy》1970,2(3):296-310
Generalizations in the canonical theory of dynamics are made; at first transformations which augment the number of canonical variables, and secondly differential transformations of the independent variable are outlined. This is applied to the perturbed two-body problem. The results are canonical systems using independent variables other than time. This leads to Delaunay-similar sets of 8 canonical elements when the Jacobian equation is separable. The application of the theory to the KS-transformation yields a completely regular canonical system in a 10-dimensional phase-space, using the eccentric anomaly as independent variable. Subsequently sets of 10 regular canonical elements are introduced.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969. 相似文献
10.
Otis F. Graf Jr. 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):321-329
The Delaunay-Similar elements of Scheifele are applied to the problem of an Earth satellite that is perturbed by the Sun, Moon andJ
2. All three effects are assumed to be the same order of magnitude. Since the external body terms depend explicitly on time, the time element appears as an additional angle variable. Also, the eccentric anomaly is used as a noncanonical auxiliary variable. A solution to the first Von Zeipel equation allows simultaneous elimination of short and intermediate period terms. The canonical transformation to mean elements is defined by a generating function that is a series involving Bessel coefficients. 相似文献
11.
The aim of this investigation is to present the secular and periodic perturbations of the six orbital elements of a close binary system due to rotational distortion. In our study we consider very small inclinationst of the orbital plane of the system, whereas the eccentricity of the orbit may assume any value between 0<e<1. The final formulae for the various elements have been expressed by means of the unperturbed true anomaly measured from the ascending node. 相似文献
12.
William Wiesel 《Celestial Mechanics and Dynamical Astronomy》1974,10(3):277-285
A perturbation series integral for the restricted problem of three bodies is derived by use of a new set of canonical elements for the regularized two-body problem. These elements are similar to theKS elements of Stiefel and Scheifele, but they contain small parameters other than the semimajor axis. The variable analogous to the longitude of perihelion not only remains well defined as the orbit approaches a circle, but also it can be used as a second small parameter. Regularized elements permit canonical use of the eccentric anomaly as independent variable, but most of the major benefits of regularization in the two-body problem do not carry over to perturbation theory. 相似文献
13.
Arnold Stokes 《Celestial Mechanics and Dynamical Astronomy》1978,17(2):137-144
When integrating a perturbed two-body problem, very often the propagation of the numerical error is reduced by using a new time variables defined by dt/ds=|q|
n
, (|q| is the radial distance,t the time). This paper introduces a time element for such transformations, i.e., a new variablet
n is defined so that dt
n/ds=1+ (perturbing terms) andt=F
n(tn), whereF
n is a known function. The time element equation should be useful in reducing the error in the determination of the timet.F
n is given explicitly forn=1, 3/2, 2, 5/2 and 3, and a general expression is given for other values.The work was performed while the author was an NRC Senior Research Associate, Goddard Space Flight Center, Greenbelt, Md., U.S.A. 相似文献
14.
J2 Invariant Relative Orbits for Spacecraft Formations 总被引：1，自引：0，他引：1
An analytic method is presented to establish J
2 invariant relative orbits. Working with mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the J2 influence. Two first order conditions are established between the differences in momenta elements (semi-major axis, eccentricity and inclination angle) that guarantee that the drift rates of two neighboring orbits are equal on the average. Differences in the longitude of the ascending node, argument of perigee and initial mean anomaly can be set at will, as long as they are setup in mean element space. For near polar orbits, enforcing both momenta element constraints may result in impractically large relative orbits. It this case it is shown that dropping the equal ascending node rate requirement still avoids considerable relative orbit drift and provides substantial fuel savings.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
15.
Piero Galeotti 《Astrophysics and Space Science》1974,31(1):193-201
The results of a spectral analysis of some high-dispersion plates of the peculiar star HR 8911 ( Piscium) are reported, and the observational evidence for somer-only elements in the atmosphere of this object is discussed.Many uranium lines were observed, so that the presence of this element may be considered certain. The presence of uranium and of some elements with mass number around theA195 peak gives strong evidence for anr-process mechanism which originated the elemental peculiarities in this object. The implications about the origin of peculiar stars are discussed on the ground of an explosive origin of ther-process elements observed in this star. Finally, the uncommon element holmium seems very likely to be present in the atmosphere of this peculiar star. 相似文献
16.
Using specialized codes for the search of periodic and linear components we show that direct solar radiation leads to short-period
variations of all the orbital elements of geosynchronous satellites. The variation period of the semimajor axis a, orbit inclination i and the longitude of the ascending node Ω is 1 day. Eccentricity e, the argument of perigee ω and the mean anomaly M vary with a period of 0.5 days. Direct solar radiation also leads to long-period variations in e, ω and M with a period of 1 year. The elements a, i and Ω undergo variations only in the amplitude of diurnal variations with a period of 1 or 0.5 years. Secular variability
(linear components) are not detected. To obtain the initial value array of the orbital elements we used the Lagrange equations
of perturbed motion in the form of a Gaussian with their subsequent integration via a special method of harmonics: the values
of the derived orbital elements, obtained from the Lagrange equations, were presented through the periodic functions that
are easy to integrate. 相似文献
17.
Andrea Milani 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):59-94
I have computed proper elements for 174 asteroids in the 1 : 1 resonance with Jupiter, that is for all the reliable orbits available (numbered and multi-opposition). The procedure requires numerical integration, under the perturbations by the four major planets, for 1,000,000 years; the output is digitally filtered and compressed into a synthetic theory (as defined within theLONGSTOP project). The proper modes of oscillation of the variables related to eccentricity, perihelion, inclination and node define proper elements. A third proper element is defined as the amplitude of the oscillation of the semimajor axis associated with the libration period; because of the strong nonlinearity of the problem, this component cannot be determined by a simple Fourier transform to the frequency domain. I therefore give another definition, which results in very good stability with time. For 87% of the computed orbits, the stability of the proper elements-at least over 1M yr-is within the following bounds: 0.001AU in semimajor axis, 0.0025 in eccentricity and sine of inclination. Half of the cases with degraded stability of the proper elements are found to be chaotic, with e-folding times between 16,000 and 660,000yr; in some other cases, chaotic behaviour does not result in a significantly decreased stability of the proper elements (stable chaos). The accuracy and stability of these proper elements is good enough to allow a search for asteroid families; however, the dynamical structure of the Trojan belt is very different from the one of the main belt, and collisional events among Trojans can result in a distribution of fragments difficult to identify. The occurrence of couples of Trojans with very close proper elements is proven not to be statistically significant in almost all cases. As the only exception, the couple 1583 Antilochus — 3801 Thrasimedes is significant; however, it is not easy to account for it by a conventional collisional theory. The Menelaus group is confirmed as a strong candidate collisional family; Teucer and Sarpedon could be considered as significant clusters. A number of other clumps are detected (by the same automated clustering method used for the main belt by Zappalà et al., 1990, 1992), but the total number of Trojans with reliable orbits is not large enough to detect many significant candidate families. 相似文献
18.
We have derived the abundances of the rare-earth elements (REEs) Ce, Pr, Nd, and Eu in the atmospheres of 26 magnetic peculiar (Ap) stars in the range of effective temperatures 7000–10 000 K from spectra with resolutions R = 48 000 and 80 000 and investigated the dependence of the CePrNdEu anomalies (the difference in the element abundances determined separately from lines of the first and second ionization stages) on the effective temperature. The REE anomaly is shown to decrease with increasing effective temperature virtually to the point of disappearance for all of the investigated elements, except Eu. For the best-studied element Nd the Nd anomaly has also been found to decrease with increasing magnetic field strength for cool stars. For hot stars there is no Nd anomaly in a wide range of magnetic field strengths. Since the presence of anomalies in cool Ap stars is associated with the REE concentration in the upper atmospheric layers, the lower boundary of the REE layer apparently sinks into deeper layers with increasing effective temperature and magnetic field, causing the anomalies to disappear. We have detected an anticorrelation between the abundances of iron-peak elements and rare-earth elements, which serves as additional evidence for different stratification of these elements in the atmospheres of Ap stars. 相似文献
19.
Using the famous Sundman inequality, we have constructed for the first time the surfaces for the general three-body problem that we suggest calling Sundman surfaces. These surfaces are a generalization of the widely known Hill surfaces in the restricted circular three-body problem. The Sundman surfaces are constructed in a rectangular coordinate system that uses the mutual distances between the bodies as the Cartesian rectangular coordinates. The singular points of the family of these surfaces have been determined. The possible and impossible regions of motion of the bodies have been constructed in the space of mutual distances. We have shown the existence of Hill stable motions and established sufficient criteria for Hill stability of motions. Some of the astronomical applications are considered. 相似文献
20.
Ram Krishan Sharma 《Celestial Mechanics and Dynamical Astronomy》1993,56(4):503-521
Analytical theory for short-term orbit motion of satellite orbits with Earth's zonal harmonicsJ
3 andJ
4 is developed in terms of KS elements. Due to symmetry in KS element equations, only two of the nine equations are integrated analytically. The series expansions include terms of third power in the eccentricity. Numerical studies with two test cases reveal that orbital elements obtained from the analytical expressions match quite well with numerically integrated values during a revolution. Typically for an orbit with perigee height, eccentricity and inclination of 421.9 km, 0.17524 and 30 degrees, respectively, maximum differences of 27 and 25 cm in semimajor axis computation are noted withJ
3 andJ
4 term during a revolution. For application purposes, the analytical solutions can be used for accurate onboard computation of state vector in navigation and guidance packages. 相似文献