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91.
Lambert problem solution in the hill model of motion 总被引:1,自引:0,他引:1
Alexander Sukhanov Antonio F. Bertachini A. Prado 《Celestial Mechanics and Dynamical Astronomy》2004,90(3-4):331-354
The goal of this paper is obtaining a solution of the Lambert problem in the restricted three-body problem described by the
Hill equations. This solution is based on the use of pre determinate reference orbits of different types giving the first
guess and defining the sought-for transfer type. A mathematical procedure giving the Lambert problem solution is described.
This procedure provides step-by-step transformation of the reference orbit to the sought-for transfer orbit. Numerical examples
of the procedure application to the transfers in the Sun–Earth system are considered. These examples include transfer between
two specified positions in a given time, a periodic orbit design, a halo orbit design, halo-to-halo transfers, LEO-to-halo
transfer, analysis of a family of the halo-to-halo transfer orbits. The proposed method of the Lambert problem solution can
be used for the two-point boundary value problem solution in any model of motion if a set of typical reference orbits can
be found. 相似文献
92.
The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977)
restricted problem of three bodies’ has been studied. In this problem one body,m
1, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ
1. The second one,m
2, is a mass point outside the shell andm
3 is a small solid sphere of densityϱ
3 supposed to be moving inside the shell subject to the attraction ofm
2 and buoyancy force due to fluidϱ
1. Here we assumem
3 to be an infinitesimal mass and the orbit of the massm
2 to be circular, and we also suppose the densitiesϱ
1, andϱ
3 to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0). 相似文献
93.
O. Ragos K. E. Papadakis C. G. Zagouras 《Celestial Mechanics and Dynamical Astronomy》1997,67(4):251-274
The regions of quasi-periodic motion around non-symmetric periodic orbits in the vicinity of the triangular equilibrium points
are studied numerically. First, for a value of the mass parameter less than Routh's critical value, the stability regions
determined by quasi-periodic motion are examined around the existing families of short (Ls
4) and long (Ll
4) period solutions. Then, for two values of μ greater than the Routh value, the unified family Lsl
4, to which, in these cases, Ls
4 and Ll
4 merge, is considered. It is found that such regions surround in general the linearly stable segments of the corresponding
families and become smaller as the mass ratio increases.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
94.
The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied.
It is found that L4,5 are unstable in the whole range 0 ≤ μ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable
for 0 < μ < μ0, where μ is the mass parameter and μ0 = 0.03852....
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
95.
96.
We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically. 相似文献
97.
98.
K.?E.?PapadakisEmail author C.?L.?Goudas G.?A.?Katsiaris 《Astrophysics and Space Science》2005,295(3):375-396
The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into
the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution
space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter
after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter),
which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain
(x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε =
0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce
the density parameter, say to ε = 10−6, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary.
The stability of all members of each and all families computed was calculated and presented in this paper for both the large
solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by
stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied
by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections.
All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received,
consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including
their stability and is available at request. It is concluded that approximation of the general solution of this system is
straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties. 相似文献
99.
A new and comprehensive method is presented that can be used for estimating eccentricity vectors between global positioning system (GPS) antennas, doppler orbitography and radiopositioning integrated by satellites (DORIS) antennas, azimuth-elevation (AZ-EL) very long baseline interferometry (VLBI) telescopes, and satellite laser ranging (SLR) and lunar laser ranging (LLR) telescopes. The problem of reference point (RP) definition for these space-geodetic instruments is addressed and computed using terrestrial triangulation and electronic distance measurement (EDM) trilateration. The practical ground operations, the surveying approach and the terrestrial data processing are briefly illustrated, and the post-processing procedure is discussed. It is a geometrically based analytical approach that allows computation of RPs along with a rigorous statistical treatment of measurements. The tight connection between the geometrical model and the surveying procedure is emphasized. The computation of the eccentricity vector and the associated variance–covariance matrix between an AZ-EL VLBI telescope (with or without intersecting axes) and a GPS choke ring antenna is concentrated upon, since these are fundamental for computing the International Terrestrial Reference Frame (ITRF). An extension to RP computation and eccentricity vectors involving DORIS, SLR and LLR techniques is also presented. Numerical examples of the quality that can be reached using the authors approach are given. Working data sets were acquired in the years 2001 and 2002 at the radioastronomical observatory of Medicina (Italy), and have been used to estimate two VLBI-GPS eccentricity vectors and the corresponding SINEX files. 相似文献
100.
GPS控制网在联测水准点的基础上,利用GPS水准高程来实现GPS网点的大地高向正常高转换,其精度主要受所拟合的似大地水准面、已知点高程和GPS网点大地高3种误差的影响。 相似文献