共查询到20条相似文献，搜索用时 15 毫秒
1.
S. M. El-Shaboury 《Astrophysics and Space Science》1990,174(1):151-154
The restricted problem of three bodies with variable masses is considered. It is assumed that the infinitesimal body is axisymmetric with constant mass and the finite bodies are spherical with variable masses such that the ratio of their masses remains constant. The motion of the finite bodies are determined by the Gyldén-Meshcherskii problem. It is seen that the collinear, triangular, and coplanar solutions not exist, but these solutions exist when the infinitesimal body be a spherical. 相似文献
2.
Arthur L. Whipple 《Celestial Mechanics and Dynamical Astronomy》1984,33(3):271-294
Fourteen equilibrium solutions of the restricted problem of 2+2 bodies are shown to exist. Six of these solutions are located about the collinear Lagrangian points of the classical restricted problem of three bodies. Eight solutions are found in the neighborhood of the triangular Lagrangian points. Linear stability analysis reveals that all of the equilibrium solutions are unstable with the exception of four solutions; two in the vicinity of each of the triangular Lagrangian points. These four solutions are found to be stable provided the mass parameter of the primary masses is less than a critical value which depends also on the mass of the minor bodies. 相似文献
3.
The restricted 2+2 body problem is considered. The infinitesimal masses are replaced by triaxial rigid bodies and the equations of motion are derived in Lagrange form. Subsequently, the equilibrium solutions for the rotational and translational motion of the bodies are detected. These solutions are conveniently classified in groups according to the several combinations which are possible between the translational equilibria and the constant orientations of the bodies. 相似文献
4.
Victor Szebehely Arthur L. Whipple 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):125-133
The restricted problem of three bodies is generalized to the restricted problem of 2+n bodies. Instead of one body of small mass and two primaries, the system is modified so that there are several gravitationally interacting bodies with small masses. Their motions are influenced by the primaries but they do not influence the motions of the primaries. Several variations of the classical problem are discussed. The separate Jacobian integrals of the minor bodies are lost but a conservative (time-independent) Hamiltonian of the system is obtained. For the case of two minor bodies, the five Lagrangian points of the classical problem are generalized and fourteen equilibrium solutions are established. The four linearly stable equilibrium solutions which are the generalizations of the triangular Lagrangian points are once again stable but only for considerably smaller values of the mass parameter of the primaries than in the classical problem. 相似文献
5.
The restricted problem of 2 + 2 bodies when one of the infinitesimal masses is further acted upon by the light pressure of the two primaries, is considered. The stationary solutions of this problem are found out. A short discussion is devoted to the stability of these solutions. 相似文献
6.
Tilemahos J. Kalvouridis 《Astrophysics and Space Science》2008,317(1-2):107-117
We deal with some new aspects of the photo-gravitational Copenhagen case of the restricted three-body problem; more particularly, the distribution and the attracting domains of the stationary solutions of small particles that move in the neighborhood of two major bodies with equal masses when one or both primaries are radiation sources with constant luminosity. Under these conditions, each particle is subjected not only to gravitational forces but to the radiation emitted from the primaries as well. 相似文献
7.
Series expansions for encounter-type solutions of Hill's problem 总被引：1，自引：0，他引：1
Hill's problem is defined as the limiting case of the planar three-body problem when two of the masses are very small. This paper describes analytic developments for encounter-type solutions, in which the two small bodies approach each other from an initially large distance, interact for a while, and separate. It is first pointed out that, contrary to prevalent belief, Hill's problem is not a particular case of the restricted problem, but rather a different problem with the same degree of generality. Then we develop series expansions which allow an accurate representation of the asymptotic motion of the two small bodies in the approach and departure phases. For small impact distances, we show that the whole orbit has an adiabatic invariant, which is explicitly computed in the form of a series. For large impact distances, the motion can be approximately described by a perturbation theory, originally due to Goldreich and Tremaine and rederived here in the context of Hill's problem. 相似文献
8.
G. N. Duboshin 《Celestial Mechanics and Dynamical Astronomy》1971,4(3-4):423-441
The particular case of the complete generalized three-body problem (Duboshin, 1969, 1970) where one of the body-points does not exert influence on the other two is analysed. These active material points act on the passive point and also on each other with forces (attraction or repulsion), proportional to the product of masses of both points and a certain function of the time, their mutual distances and their first and second derivatives. Furthermore it is not supposed that generally the third axiom of mechanics (action=reaction) takes place.Here under these more general assumptions the equations of motion of the active masses and the passive point, as well as the diverse transformations of these equations are analogous of the same transformations which are made in the classical case of the restricted three-body problem.Then we determine conditions for some particular solutions which exist, when the three points form the equilateral triangle (Lagrangian solutions) or remain always on a straight line (Eulerian solutions).Finally, assuming that some particular solutions of the above kind exist, the character of solutions near this particular one is envisaged. For this purpose the general variational equations are composed and some conclusions on the Liapunov stability in the simplest cases are made. 相似文献
9.
Special analytical solutions are determined for restricted, coplanar, four-body equal mass problems, including the Caledonian problem, where the masses Mi = M for i = 1,2,3,4. Most of these solutions are shown to reduce to the Lagrange solutions of the Copenhagen problem of three bodies by reducing two of the masses (mi = m for i = 1,2) in the four-body equal mass problem to zero while maintaining their equality of mass. In so doing, families of special solutions to the four-body problem are shown to exist for any value of the mass ratio μ = m/M. 相似文献
10.
Esther Barrabés Josep Maria Cors Conxita Pinyol Jaume Soler 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):55-66
Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame. 相似文献
11.
We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler
central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in
the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration,
the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and
fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to
the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the
three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with
four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass
at the midpoint of one of the parallel sides. 相似文献
12.
T.J. Kalvouridis 《Astrophysics and Space Science》1998,259(1):77-90
The restricted gravitational 2 + 2 body problem, is a particular case of the N body problem and it may be used to approximate
the dynamical behaviour of binary asteroids or dual sattelites moving in the gravitational field of two primaries Pi, i =
1,2. By considering oblate primaries, five parameters are needed to describe the model, namely the reduced mass μ of the primary
P2, the reduced masses μ1 and μ2 of the minor bodies and the oblatenesses Ii, i = 1,2 of the primaries. This work deals with
the effect of those parameters on the location of the stationary solutions.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
S. M. Elshaboury 《Astrophysics and Space Science》1991,186(2):245-251
The restricted problem of a tri-axial rigid body and two spherical bodies with variable masses be considered. The general solution of the equations of motion of the tri-axial body be obtained in which the motion of the spherical bodies is determined by the classic nonsteady Gyldén-Meshcherskii problem. 相似文献
14.
A complete solution is given for a symmetric case of the problem of the planar central configurations of four bodies, when two bodies are on an axis of symmetry, and the other two bodies have equal masses and are situated symmetrically with respect to the axis of symmetry. The positions of the bodies on the axis of symmetry are described by angle coordinates with respect to the outside bodies. The solution is such, that giving the angle coordinates, the masses for which the given configuration is a central configuration, can be computed from simple analytical expressions of the angles. The central configurations can be described as one-parameter families, and these are discussed in detail in one convex and two concave cases. The derived formulae represent exact analytical solutions of the four-body problem. 相似文献
15.
The article contains a numerical study of periodic solutions of the Planar General Three-Body Problem. Several new periodic solutions have been discovered and are described. In particular, there is a continuous family with variable masses, extending all the way from the elliptic restricted problem to the general problem with three equal masses. All our examples have special symmetry properties which are described in detail. Finally we also suggest some important applications to the natural satellites of the solar system. 相似文献
16.
Carles Simó 《Celestial Mechanics and Dynamical Astronomy》1978,18(2):165-184
Beyond the casen=3 little was known about relative equilibrium solutions of then-body problem up to recent years. Palmore's work provides in the general case much useful information. In the casen=4 he gives the totality of solutions when the four masses are equal and studies some degeneracies. We present here a survey of solutions for arbitrary masses, discussing the manifolds of degeneracy. The ordering of restricted potentials allows a counting of the number of bifurcation sets and different invariant manifolds. An analysis of linear stability is done in the restricted and general cases. As a result, values of the masses ensuring linear stability are given. 相似文献
17.
The restricted problem of 2+2 bodies is applied to the study of the stability and dynamics of binary asteroids in the solar system. Numerical investigation of the behavior of the orbital elements and the maximal Lyapunov characteristic number of binary asteroids reveal extensive regions where bounded quasiperiodic motion is possible. These regions are compared to the bounded regions which are predicted by the classical restricted problem of three bodies. Regions of bounded chaotic solutions are also found. 相似文献
18.
L. G. Luk’yanov 《Astronomy Letters》2009,35(5):349-359
We consider the restricted circular three-body problem in which the main bodies have variable masses but the sum of their masses always remains constant. For this problem, we have obtained the possible regions of motions of the small body and the previously unknown surfaces of minimum energy that bound them using the Jacobi quasi-integral. For constant masses, these surfaces transform into the well-known surfaces of zero velocity. We consider the applications of our results to close binary star systems with conservative mass transfer. 相似文献
19.
John D. Hadjidemetriou 《Astrophysics and Space Science》1976,40(1):201-224
Several families of the planar general three-body problem for fixed values of the three masses are found, in a rotating frame of reference, where the mass of two of the bodies is small compared to the mass of the third body. These families were obtained by the continuation of a degenerate family of periodic orbits of three bodies where two of the bodies have zero masses and describe circular orbits around a third body with finite mass, in the same direction.The above families represent planetary systems with the body with the large mass representing the Sun and the two small bodies representing two planets or comets. One section of a family is shown to represent the Jupiter family of comets and also a model for the Sun-Jupiter-Saturn system is found.The stability analysis revealed that stability exists for small masses and small eccentricities of the two planets. Planetary systems with relatively large masses and eccentricities are proved to be unstable. In particular, the Jupiter family of comets, for small masses of the two small bodies, and the Sun-Jupiter-Saturn system are proved to be stable. Also, it was shown that resonances are not necessarily associated with instabilities. 相似文献
20.
Solar System Research - The outer version of the restricted elliptic three-body problem, where a perturbed body of negligible mass is far from two bodies of finite masses (the main and perturbing... 相似文献