共查询到20条相似文献，搜索用时 31 毫秒
1.
Kiyotaka Tanikawa Hiroaki Umehara Hiroshi Abe 《Celestial Mechanics and Dynamical Astronomy》1995,62(4):335-362
A numerical procedure is devised to find binary collision orbits in the free-fall three-body problem. Applying this procedure, families of binary collision orbits are found and a sequence of triple collision orbits are positioned. A property of sets of binary collision orbits which is convenient to search triple collision orbits is found. Important numerical results are formulated and summarized in the final section. 相似文献
2.
The planar isosceles three-body problem where the two symmetric bodies have small masses is considered as a perturbation of
the Kepler problem. We prove that the circular orbits can be continued to saddle orbits of the Isosceles problem. This continuation
is not possible in the elliptic case. Their perturbed orbits tend to a continued circular one or approach a triple collision.
The basic tool used is the study of the Poincaré maps associated with the periodic solutions.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
K. C. Howell 《Celestial Mechanics and Dynamical Astronomy》1987,40(3-4):393-407
A timing condition for consecutive collision orbits in the planar, circular three-body problem has been extended to the elliptic restricted problem for =0. The expression developed relates eccentric anomalies at the time of collision. Some families of solutions are presented. 相似文献
4.
5.
We consider the particular case of the planar three body problem obtained when the masses form an isosceles triangle for all time. Various authors [1, 2, 12, 8, 9, 13, 10] have contributed in the knowledge of the triple collision and of several families of periodic orbits in this problem. We study the flow on a fixed level of negative energy. First we obtain a topological representation of the energy manifold including the triple collision and infinity as boundaries of that manifold. The existence of orbits connecting the triple collision and infinity gives some homoclinic and heteroclinic orbits. Using these orbits and the homothetic solutions of the problem we can characterize orbits which pass near triple collision and near infinity by pairs of sequences. One of the sequences describes the regions visited by the orbit, the other refers to the behaviour of the orbit between two consecutive passages by a suitable surface of section. This symbolic dynamics which has a topological character is given in an abstract form and after it is applied to the isosceles problem. We try to keep globality as far as possible. This strongly relies on the fact that the intersection of some invariant manifolds with an equatorial plane (v=0) have nice spiraling properties. This can be proved by analytical means in some local cases. Numerical simulations given in Appendix A make clear that these properties hold globally. 相似文献
6.
Consecutive collision orbits in the limiting case µ = 0 of the elliptic restricted three-body problem are investigated. in particular those in which the infinitesimal mass collides twice with the smaller (massless) primary. A timing condition is presented that allows the extension of previous results to the case of arbitrary relative orientation of the orbits of the infinitesimal mass and the smaller primary. The timing condition is expressed in two general forms - in terms of orbit parameters and eccentric (or hyperbolic) anomalies at the times of collision - for the specific cases of elliptic. parabolic or hyperbolic orbits of the infinitesimal mass. Some families of solutions are presented. 相似文献
7.
We study symmetric relative periodic orbits in the isosceles three-body problem using theoretical and numerical approaches.
We first prove that another family of symmetric relative periodic orbits is born from the circular Euler solution besides
the elliptic Euler solutions. Previous studies also showed that there exist infinitely many families of symmetric relative
periodic orbits which are born from heteroclinic connections between triple collisions as well as planar periodic orbits with
binary collisions. We carry out numerical continuation analyses of symmetric relative periodic orbits, and observe abundant
families of symmetric relative periodic orbits bifurcating from the two families born from the circular Euler solution. As
the angular momentum tends to zero, many of the numerically observed families converge to heteroclinic connections between
triple collisions or planar periodic orbits with binary collisions described in the previous results, while some of them converge
to “previously unknown” periodic orbits in the planar problem. 相似文献
8.
Florin Nicolae Diacu 《Celestial Mechanics and Dynamical Astronomy》1990,50(4):313-324
We show that every planar isosceles solution of the three-body problem encounters a collision of the symmetric particles, either forwards or backwards in time. Regularizing analytically this collision, the solution has at least a syzygy configuration and/or leads to a total collapse. Some further simple results support the intuitive image on the tame local behavior of the motion as long as it does not lead to a triple collision. As a main result we prove that total collapse singularities, can be regularized in aC 1-fashion with respect to time, for all values of the masses. Using symbolic dynamics, the chaotic character of theC 1-regularized solutions is pointed out. 相似文献
9.
The isosceles rectilinear restricted three-body problem can be considered as the Sitnikov's problem with eccentricity one
or, as the isosceles problem when the central mass is zero and the primaries move having consecutive elliptic collisions.
We compactify the phase space and analyze the flow on their boundary. This allows us to separate the phase space into different
regions depending on the kind of orbits.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
Dominant factors for escape after the first triple-encounter are searched for in the three-body problem with zero initial
velocities and equal masses. By a global numerical survey on the whole initial-value space, it is found that not only a triple-collision
orbit but also a particular family of binary-collision orbits exist in the set of escape orbits. This observation is justified
from various viewpoints. Binary-collision orbits experiencing close triple-encounter turn out to be close to isosceles orbits
after the encounter and hence lead to escape. Except for a few cases, binary-collision orbits of near-isosceles slingshot
also escape.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
11.
We consider the motions of particles in the one-dimensional Newtonian three-body problem as a function of initial values.
Using a mapping of orbits to symbol sequences we locate the initial values leading to triple collisions. These turn out to
form curves which give clear structure to the region in which the motions depend sensitively on initial conditions. In addition
to finding the triple collision orbits we also locate orbits which end up to a triple collision in both directions of time,
that is, orbits which are finite both in space and time.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
The existence of escape and nonescape orbits arbitrarily close to the homothetic equilateral triplecollision orbit is considered analytically in the threebody problem with zero initial velocities and equal masses. It is proved that escape orbits in the initial condition space are distributed around three kinds of isosceles orbits. It is also proved that nonescape orbits are distributed in between the escape orbits where different particles escape. In order to show this, it is proved that the homotheticequilateral orbit is isolated from other triplecollision orbits as far as the collision at the first triple encounter is concerned. Moreover, the escape criterion is formulated in the planarisosceles problem and translated into the words of regularizing variables. The result obtained by us explains the orbital structure numerically. 相似文献
13.
P. Delibaltas 《Celestial Mechanics and Dynamical Astronomy》1983,29(2):191-204
In the general three-body problem, in a rotating frame of reference, a symmetric periodic solution with a binary collision is determined by the abscissa of one body and the energy of the system. For different values of the masses of the three bodies, the symmetric periodic collision orbits form a two-parametric family. In the case of equal masses of the two bodies and small mass of the third body, we found several symmetric periodic collision orbits similar to the corresponding orbits in the restricted three-body problem. Starting with one symmetric periodic collision orbit we obtained two families of such orbits. Also starting with one collision orbit in the Sun-Jupiter-Saturn system we obtained, for a constant value of the mass ratio of two bodies, a family of symmetric periodic collision orbits. 相似文献
14.
Masaya Masayoshi Saito Kiyotaka Tanikawa 《Celestial Mechanics and Dynamical Astronomy》2010,107(4):397-407
In the present paper, in the rectilinear three-body problem, we qualitatively follow the positions of non-Schubart periodic
orbits as the mass parameter changes. This is done by constructing their characteristic curves. In order to construct characteristic
curves, we assume a set of properties on the shape of areas corresponding to symbol sequences. These properties are assured
by our preceding numerical calculations. The main result is that characteristic curves always start at triple collision and
end at triple collision. This may give us some insight into the nature of periodic orbits in the N-body problem. 相似文献
15.
E. A. Belbruno 《Celestial Mechanics and Dynamical Astronomy》1981,25(4):397-415
A new regularizing transformation for the three-dimensional restricted three-body problem is constructed. It is explicitly derived and is equivalent to a simple rational map. Geometrically it is equivalent to a rotation of the 3-sphere. Unlike the KS map it is dimension preserving and is valid inn dimensions. This regularizing map is applied to the restricted problem in order to prove the existence of a family of periodic orbits which continue from a family of collision orbits. 相似文献
16.
The present work investigates a mechanism of capturing processes in the restricted three-body problem. The work has been done in a set of variables which is close to Delaunay's elements but which allows for the transition from elliptic to hyperbolic orbits. The small denominator difficulty in the perturbation theory is overcome by embedding the small denominator in an analytic function through a suitable analytic continuation. The results indicate that motions in nearly parabolic orbits can become chaotic even though the model is deterministic. The theoretical results are compared with numerical results, showing an agreement of about one percent. Some possible applications to cometary orbits are also given. 相似文献
17.
Robert L. Devaney 《Celestial Mechanics and Dynamical Astronomy》1982,28(1-2):25-36
We describe in detail the qualitative behavior of solutions of the planar isosceles problem which come close to triple collision. Using a method of McGehee, one may describe a neighborhood of triple collision for any mass ratios. For sufficiently small mass ratios, we exhibit infinitely many distinct periodic and collision/ejection solutions of this problem.Partially supported by N.S.F. Grant MCS 81-01855.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics. 相似文献
18.
V. V. Orlov A. V. Petrova A. I. Martynova 《Monthly notices of the Royal Astronomical Society》2002,333(3):495-500
The general plane isosceles three-body problem is considered for different ratios of the central body mass to the masses of other bodies. The central body goes through the middle of the segment connecting the other bodies along the perpendicular to this segment. The initial conditions are chosen by two parameters: the virial ratio k and the parameter , where r˙ is the relative velocity of the 'outer' bodies, and R˙ is the velocity of the 'central' body with respect to the mass centre of the 'outer' bodies. The equations of motion are numerically integrated until one of three times: the time of escape of the central body, its time of ejection with R >100 d , or 1000 τ (here d is the mean size, and τ is the mean crossing time of the triple system). The regions corresponding to escapes of the central body after different numbers of triple approaches are found at the plane of parameters k ∈(0,1) and μ ∈(-1,1) . The regions of stable motions are revealed. The zones of regular and stochastic orbits are outlined. The fraction of stochastic trajectories increases with the central mass. The fraction of stable orbits is highest for equal masses of the bodies. 相似文献
19.
Martin Lara 《Celestial Mechanics and Dynamical Astronomy》2017,127(3):285-300
This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions. 相似文献
20.
A new family of periodic orbits for the restricted problem 总被引：1，自引：0，他引：1
E. A. Belbruno 《Celestial Mechanics and Dynamical Astronomy》1981,25(2):195-217
A new family of periodic orbits of the three-dimensional restricted three-body problem which continue off from a consecutive collision orbit are numerically studied. Their behavior for varying energy is unexpected. In particular, associated with our system is a countable set of resonant energy values and each time the energy passes through one of them the periodic orbit forms a loop by self-intersection. Any number of loops can form by this process and the resulting orbits take on an interesting appearance. 相似文献