共查询到20条相似文献，搜索用时 812 毫秒
1.
The energy and the angular momentum integral of motion for the planar three point problem cannot assure bounded motion. In this paper it is shown that if one of the points is replaced by a homogeneous sphere then bounded motion can be found. The zero velocity surfaces for this modified problem are found and their evolution is described. 相似文献
2.
H. M. Yehia 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):275-288
The general problem of motion of a rigid body about a fixed point under the action of stationary non-symmetric potential and gyroscopic forces is considered. The equations of motion in the Euler-Poisson form are derived. An interpretation is given in terms of charged, magnetized gyrostat moving in a superposition of three classical fields. As an example, the problem of motion of a satellite — gyrostat on a circular orbit with respect to its orbital system is reduced to that of its motion in an inertial system under additional magnetic and Lorentz forces.When the body is completely symmetric about one of its axes passing through the fixed point, the above problem is found to be equivalent to another one, in which the body has three equal moments of inertia and the forces are symmetric around a space axis. The last problem is well-studied and the given analogy reveals a number of integrable cases of the original problem. A transformation is found, which gives from each of these cases a class of integrable cases depending on an arbitrary function. The equations of motion are also reduced to a single equation of the second order. 相似文献
3.
4.
The plane, singly averaged, elliptical restricted three body problem is considered in the article. The first three terms are taken in the perturbing function. The equations of motion in terms of the canonical elements of Delaunay are obtained. And the change of the elements of motion of the satellite due to the perturbing function is calculated. An application is given in the case of a satellite in the earth-moon system. 相似文献
5.
6.
Kyle T. Alfriend 《Celestial Mechanics and Dynamical Astronomy》1972,5(4):502-511
The question of whether or not there is a transfer of energy between the in-plane motion and out-of-plane motion in the neighborhood ofL
4 in the restricted problem of three bodies is investigated in this paper. The in-plane motion is assumed to be finite and the out-of-plane motion to be infinitesimal. The equation governing the out-of-plane motion becomes one with time varying coefficients. The stability of this equation is then investigated using Lie Series.Presented as a paper AAS No. 70-313, at the AAS/AIAA Astrodynamics Specialists Conference 1971 at Fort Lauderdale Fla., U.S.A. 相似文献
7.
Jörg Waldvogel 《Celestial Mechanics and Dynamical Astronomy》1975,11(4):429-432
A new method is described for representing the motion in the planar problem of three bodies when all three point masses simultaneously come close to each other. The main results are (1) that the motion during the critical phase of closest approach is intimately connected with triple parabolic escape and (2) that a sufficiently close triple approach generally leads to the escape of one body witharbitrarily high asymptotic velocity. 相似文献
8.
Marcello Romano 《Celestial Mechanics and Dynamical Astronomy》2008,100(3):181-189
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of
inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary
initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular,
the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points
on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type,
which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent
hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic
map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found
analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to
the small set of special cases for which an exact solution of the rotational motion of a rigid body exists. 相似文献
9.
V. A. Shefer 《Astronomy Letters》2007,33(4):270-282
We suggest a new approach to solving the problem of finding the orbit of a celestial body from its three spatial position vectors and the corresponding times. It allows most of the perturbations in the motion of a celestial body to be taken into account. The approach is based on the theory of intermediate orbits that we developed previously. We construct the orbit the motion along which is a combination of two motions: the motion of a fictitious attracting center whose mass varies according to Mestschersky’s first law and the motion relative to the fictitious center. The first motion is generally parabolic, while the second motion is described by the equations of the Gylden-Mestschersky problem. The constructed orbit has such parameters that their limiting values at any reference epoch define a superosculating intermediate orbit with a fourth-order tangency. We have performed a numerical analysis to estimate the accuracy of approximating the perturbed motion of two minor planets, 145 Adeona and 4179 Toutatis, by the orbits computed using two-position procedures (the classical Gauss method and the method that we suggested previously), a three-position procedure based on the Herrick-Gibbs equation, and the new method. Comparison of the results obtained suggests that the latter method has an advantage. 相似文献
10.
Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》1994,60(1):57-68
A new canonical transformation of freedom two was found. By using this, we derived three new sets of canonical variables for the orbital motion and two for the rotational motion. New canonical variables have clear physical meanings and remain well-defined in the case when the classical sets become ill-defined, for example, when the eccentricity and/or the inclination is small for the elliptic orbital motion. 相似文献
11.
V. A. Shefer 《Solar System Research》2010,44(2):152-165
We propose a new method for the determination of the preliminary orbit of a small celestial body using three pairs of its
angular coordinates in three moments of time. The method is based on the use of the intermediate orbit we constructed earlier
using three position vectors and the corresponding time moments. This intermediate orbit accounts for the main part of the
perturbations of the motion of the body under study. We compare the results obtained by the classical Lagrange-Gauss method,
Herrick-Gibbs method, generalized Herrick-Gibbs method, and the new method by the examples of the determination of the orbit
of the small planet 1566 Icarus. The comparison showed that the new method is a highly efficient tool for the study of perturbed
motion. It is especially efficient when applied to high-precision observational data covering short arcs of the orbit. 相似文献
12.
《New Astronomy》2020
The objective of this paper is to find periodic solutions of the circular Sitnikov problem by the multiple scales method which is used to remove the secular terms and find the periodic approximated solutions in closed forms. Comparisons among a numerical solution (NS), the first approximated solution (FA) and the second approximated solution (SA) via multiple scales method are investigated graphically under different initial conditions. We observe that the initial conditions play a vital role in the numerical and approximated solutions behaviour. The obtained motion is periodic, but the difference of its amplitude is directly proportional with the initial conditions. We prove that the obtained motion by the numerical or the second approximated solutions is a regular and periodic, when the infinitesimal body starts its motion from a nearer position to the common center of primaries. Otherwise when the start point distance of motion is far from this center, the numerical solution may not be represent a periodic motion for along time, while the second approximated solution may present a chaotic motion, however it is always periodic all time. But the obtained motion by the first approximated solution is periodic and has regularity in its periodicity all time. Finally we remark that the provided solutions by multiple scales methods reflect the true motion of the Sitnikov restricted three–body problem, and the second approximation has more accuracy than the first approximation. Moreover the solutions of multiple scales technique are more realistic than the numerical solution because there is always a warranty that the motion is periodic all time. 相似文献
13.
Comparative Study of the 2:3 and 3:4 Resonant Motion with Neptune: An Application of Symplectic Mappings and Low Frequency Analysis 总被引：2，自引：1，他引：1
The 2:3 and 3:4 exterior mean motion resonances with Neptune are studied by applying symplectic mapping models. The mappings
represent efficiently Poincaré maps for the 3D elliptic restricted three body problem in the neighbourhood of the particular
resonances. A large number of trajectories is studied showing the coexistence of regular and chaotic orbits. Generally, chaotic
motion depletes the small bodies of the effective resonant region in both the 2:3 and 3:4 resonances. Applying a low frequency
spectral analysis of trajectories, we determined the phase space regions that correspond to either regular or chaotic motion.
It is found that the phase space of the 3:4 resonant motion is more chaotic than the 2:3 one. 相似文献
14.
In this paper we have deduced the differential equations of motion of the restricted problem of three bodies with decreasing mass, under the assumption that the mass of the satellite varies with respect to time. We have applied Jeans law and the space time transformation contrast to the transformation of Meshcherskii. The space time transformation is applicable only in the special casen=1,k=0,q=1/2. The equations of motion of our problem differ from the equations of motion of the restricted three body problem with constant mass only by small perturbing forces. 相似文献
15.
Jin Ma Yong-Hong Zhou De-Chun Liao Jian-Li Chen Shanghai Astronomical Observatory Chinese Academy of Sciences Shanghai Graduate School of Chinese Academy of Sciences Beijing Center for Space Research University of Texas at Austin Austin TX USA 《中国天文和天体物理学报》2007,7(6):831-838
The global oceans play important roles in exciting the annual polar motion besides the atmosphere. However,it is still unclear about how large the regional oceans contribute to the annual polar motion. We investigate systemically the contributions of the Pacific,Atlantic and Indian Oceans to the excitation of the annual polar motion,based on the output data of ocean current velocity field and ocean bottom pressure field from "Estimating the Circulation and Climate of the Ocean (ECCO)" ocean circulation model over the period 1993-2005. The result shows that due to its particular location and shape,the Atlantic Ocean makes a less significant contribution to the x-component of the annual polar motion excitation than the Pacific and Indian Oceans,while all these three oceans contribute to the y-component of the annual polar motion excitation to some extent. 相似文献
16.
W. J. Robinson 《Celestial Mechanics and Dynamical Astronomy》1973,8(2):323-330
This paper is concerned with an extension of the classical restricted problem of three bodies in three dimensions. Usually, the satellite is considered to be a point mass. Here, the satellite is assumed to have a simple structure. The equations of motion are obtained and some of their consequences are discussed. 相似文献
17.
《天文和天体物理学研究(英文版)》2017,(4)
A new non-simplified model of formation flying is derived in the presence of an oblate mainbody and third-body perturbation.In the proposed model,considering the perturbation of the thirdbody in an inclined orbit,the effect of obliquity(axial tilt) of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite.From a new point of view,J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit,are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion.To validate the accuracy of the model presented in this study,an auxiliary model was constructed as the Main-body Center based Relative Motion(MCRM) model.Finally,the importance of the main-body's obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping.The main-body's obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit(PCO) formations. 相似文献
18.
19.
The literal solution of the restricted three body problem obtained by the authors up to the eleventh order with respect to the minor parameter is applied to the investigation of the motion of Phoebe, the ninth satellite of Saturn. As distinct from the existing analytical theories of the motion of the satellite, in the present paper the planetary perturbations are taken into account. A comparison with the modern numerical theory of the motion of Phoebe has shown that the new analytical theory of the satellite motion represents observations with the same degree of accuracy. 相似文献
20.
We have considered the problem of the propagation of nonzero rest-mass neutrinos in the Friedmann dust universes of three types: open, flat, and closed, as well as in the radiation-dominated epoch of thehot universe. The total Lagrangian path of the particle has been calculated, and this is shown to be finite for all the three universes-contrary to the total path of the photon, which is infinite in the open and flat universes.We have found the particle horizon as a function of the relativistic parameter at the emission moment and at the moment of observation. The extreme relativistic and nonrelativistic particle motion and its difference from the photon motion have been investigated. 相似文献