共查询到20条相似文献,搜索用时 15 毫秒
1.
Joanna P. Anosova 《Celestial Mechanics and Dynamical Astronomy》1991,51(1):1-15
Strong three-body interactions play a decisive role in the course of the dynamical evolution of triple systems having positive
as well as negative total energies. These interactions may produce qualitative changes in the relative motions of the components.
In triple systems with positive or zero total energies the processes of formation, disruption or exchange of the components
of binaries take place as the result of close approaches of the three single bodies or as the result of the passages of single
bodies past wide or hard binaries. In the triple systems with negative energies, the strong triple interactions may result
in an escape from the system as well as a formation of a hard final binary.
This paper summarizes the general results of the studies of the strong three-body interactions in the triple systems with
positive and negative energies. These studies were conducted at the Leningrad University Observatory by computer simulations
during 1968–1989. 相似文献
2.
The dynamical evolution of triple systems with equal and unequal-mass components and different initial velocities is studied. It is shown that, in general, the statistical results for the planar and three-dimensional triple systems do not differ significantly. Most (about 85%) of the systems disrupt; the escape of one component occurs after a triple approach of the components. In a system with unequal masses, the escaping body usually has the smallest mass. A small fraction (about 15%) of stable or long-lived systems is formed if the angular momentum is non-zero. Averages, distributions and coefficients of correlations of evolutionary characteristics are presented: the life-time, angular momentum, numbers of wide and close triple approaches of bodies, relative energy of escapers, minimum perimeter during the last triple approach resulting in escape, elements of orbits of the final binary and escaper. 相似文献
3.
The dynamical evolution of triple systems has been studied by computer simulations. A function (t) has been defined, where p is the maximum distance of the components from their centre of inertia, and t is the time. The value of is used to indicate the current size of the triple system. The minima of have been followed during the course of evolution of the triples. A distribution of f(min) has been obtained, which is described by the following statistical parameters: the mode is equal to 0.65d, the mean value min= 0.750d, r.m.s. is 0.477d, the asymmetry is 0.218, the excess is 2.04 where d is the mean harmonic distance between the bodies in the equilibrium state of the triple system. As a rule, escapes from triples occur only after close three-body approaches. 相似文献
4.
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
5.
J. P. Anosova V. V. Orlov S. J. Aarseth 《Celestial Mechanics and Dynamical Astronomy》1994,60(3):365-372
The dynamical evolution of triple systems with equal-mass components and zero initial velocities is studied. We consider two regions of initial conditions: a regionD of all possible configurations of triples and a circleR. The configurations are distributed uniformly within these regions. The calculations have been carried out until a time when escape or conditional escape (i.e. distant ejection) of one component takes place. The accuracy has been checked by doing time-reversed integration. Types of predictable and non-predictable systems are revealed. Averages for a number of evolution parameters are presented: the life-time, minimum perimeter during the last triple approach resulting in escape, semi-major axis and eccentricity of the final binary, and the smallest separation between the components during the evolution. It is shown that the statistical results for the regionsD andR do not differ significantly for the most part. Our results, which have been obtaned by a three-body regularization method, are in good agreement with previous work based on the RK4 integrator and Sundman's time smoothing. 相似文献
6.
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
7.
S. J. Aarseth J. P. Anosova V. V. Orlov V. G. Szebehely 《Celestial Mechanics and Dynamical Astronomy》1994,58(1):1-16
The effects of small changes in the initial conditions of the Pythagorean three-body problem are investigated by computer simulations. This problem consists of three interacting bodies with masses 3, 4 and 5 placed with zero velocities at the apices of a triangle with sides 3, 4 and 5. The final outcome of this motion is that two bodies form a binary and the third body escapes. We attempt to establish regions of the initial positions which give regular and chaotic motions. The vicinity of a small neighbourhood around the standard initial position of each body defines a regular region. Other regular regions also exist. Inside these regions the parameters of the triple systems describing the final outcome change continuously with the initial positions. Outside the regular regions the variations of the parameters are abrupt when the initial conditions change smoothly. Escape takes place after a close triple approach which is very sensitive to the initial conditions. Time-reversed solutions are employed to ensure reliable numerical results and distinguish between predictable and non-predictable motions. Close triple approaches often result in non-predictability, even when using regularization; this introduces fundamental difficulties in establishing chaotic regions. 相似文献
8.
The equations of motion of the planar three-body problem split into two parts, called an external part and an internal part. When the third mass approaches zero, the first part tends to the equations of the Kepler motion of the primaries and the second part to the equations of motion of the restricted problem.We discuss the Hill stability from these equations of motion and the energy integral. In particular, the Jacobi integral for the circular restricted problem is seen as an infinitesimal-mass-order term of the Sundman function in this context. 相似文献
9.
Masaya Masayoshi Saito Kiyotaka Tanikawa 《Celestial Mechanics and Dynamical Astronomy》2007,98(2):95-120
The dynamical structure of phase space of gravitational Newtonian three bodies which lie on a line (rectilinear three-body
system) is studied. We take an initial value plane and classify the points on the plane according to the fate of the orbits
starting from the points, using symbol sequences. The structure appearing on the initial value plane with this classification
was well studied for the equal-mass case (Tanikawa and Mikkola 2000, Chaos 10, 649–657). In this paper, we follow and clarify the changes of this structure with the mass ratio of three particles. 相似文献
10.
Victor Vladimirovich Orlov Anna V. Petrova Kiyotaka Tanikawa Masaya M. Saito Alija I. Martynova 《Celestial Mechanics and Dynamical Astronomy》2008,100(2):93-120
The rectilinear equal-mass and unequal-mass three-body problems are considered. The first part of the paper is a review that
covers the following items: regularization of the equations of motion, integrable cases, triple collisions and their vicinities,
escapes, periodic orbits and their stability, chaos and regularity of motions. The second part contains the results of our
numerical simulations in this problem. A classification of orbits in correspondence with the following evolution scenarios
is suggested: ejections, escapes, conditional escapes (long ejections), periodic orbits, quasi-stable long-lived systems in
the vicinity of stable periodic orbits, and triple collisions. Homothetic solutions ending by triple collisions and their
dependence on initial parameters are found. We study how the ejection length changes in response to the variation of the triple
approach parameters. Regions of initial conditions are outlined in which escapes occur after a definite number of triple approaches
or a definite time. In the vicinity of a stable Schubart periodic orbit, we reveal a region of initial parameters that corresponds
to trajectories with finite motions. The regular and chaotic structure of the manifold of orbits is mostly defined by this
periodic orbit. We have studied the phase space structure via Poincaré sections. Using these sections and symbolic dynamics,
we study the fine structure of the region of initial conditions, in particular the chaotic scattering region. 相似文献
11.
Evan S. Gawlik Jerrold E. Marsden Philip C. Du Toit Stefano Campagnola 《Celestial Mechanics and Dynamical Astronomy》2009,103(3):227-249
This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP),
a generalization of the circular restricted three-body problem (CR3BP) that asks for the motion of a test particle in the
presence of two elliptically orbiting point masses. Previous studies demonstrate that an understanding of transport phenomena
in the CR3BP, an autonomous dynamical system (when viewed in a rotating frame), can be obtained through analysis of the stable
and unstable manifolds of certain periodic solutions to the CR3BP equations of motion. These invariant manifolds form cylindrical
tubes within surfaces of constant energy that act as separatrices between orbits with qualitatively different behaviors. The
computation of LCS, a technique typically applied to fluid flows to identify transport barriers in the domains of time-dependent
velocity fields, provides a convenient means of determining the time-dependent analogues of these invariant manifolds for
the ER3BP, whose equations of motion contain an explicit dependency on the independent variable. As a direct application,
this study uncovers the contribution of the planet Mercury to the Interplanetary Transport Network, a network of tubes through
the solar system that can be exploited for the construction of low-fuel spacecraft mission trajectories.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
12.
Capture and escape in the elliptic restricted three-body problem 总被引:1,自引:0,他引:1
Sergey A. Astakhov David Farrelly 《Monthly notices of the Royal Astronomical Society》2004,354(4):971-979
13.
Vladimir N. Shinkin 《Celestial Mechanics and Dynamical Astronomy》1995,62(4):323-334
For the general three-body problem at third-order resonance an analytical solution is obtained by the use of the Weierstrass functions. 相似文献
14.
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
15.
Alexei V. Tsygvintsev 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):23-29
We consider the Newtonian planar three-body problem with positive masses m
1, m
2, m
3. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian
orbit besides three exceptional cases ∑m
i
m
j
/(∑m
k
)2 = 1/3, 23/33, 2/32 where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis
of the three-body problem started in papers [Tsygvintsev, A.: Journal für die reine und angewandte Mathematik N 537, 127–149
(2001a); Celest. Mech. Dyn. Astron. 86(3), 237–247 (2003)] and based on the Morales–Ramis–Ziglin approach. 相似文献
16.
Masaya Masayoshi Saito Kiyotaka Tanikawa 《Celestial Mechanics and Dynamical Astronomy》2009,103(3):191-207
We study the change of phase space structure of the rectilinear three-body problem when the mass combination is changed. Generally,
periodic orbits bifurcate from the stable Schubart periodic orbit and move radially outward. Among these periodic orbits there
are dominant periodic orbits having rotation number (n − 2)/n with n ≥ 3. We find that the number of dominant periodic orbits is two when n is odd and four when n is even. Dominant periodic orbits have large stable regions in and out of the stability region of the Schubart orbit (Schubart
region), and so they determine the size of the Schubart region and influence the structure of the Poincaré section out of
the Schubart region. Indeed, with the movement of the dominant periodic orbits, part of complicated structure of the Poincaré
section follows these orbits. We find stable periodic orbits which do not bifurcate from the Schubart orbit. 相似文献
17.
Sufficient conditions are given for the escape of a member of a three-body system. The set of conditions are similar to those given previously by Tevzadze (1962). The new set compares favorably in most cases with that of Tevzadze. 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.
The envelope of iso-energetic trajectories in the (repulsive) two-fixed-centre problem is derived. Our analytical calculations finally lead to a transcendental equation, only containing elliptic integrals and the Weierstraßp function, from which the envelope is constructed. The results may serve as a simple model for the boundary layer between two colliding supersonic stellar wind flows in binary systems, in which at least one of the components has a strong radiation field.Beyond this, the effect of non-inertial forces (centrifugal and Coriolis force) due to the binary's orbital motion has been estimated by a numerical analysis within the scope of the (repulsive) restricted three-body problem.All calculations have been performed for a hot model (Wolf-Rayet/O-star) binary system with a set of parameters which might be appropriate for HD 152270. The envelope may be well approximated by a hyperboloid. The non-inertial forces slightly turn the envelope against the line connecting both stars. 相似文献
20.
An analytical proof of the existence of some kinds of periodic orbits of second species of Poincaré, both in the Circular and Elliptic Restricted three-body problem, is given for small values of the mass parameter. The proof uses the asymptotic approximations for the solutions and the matching theory developed by Breakwell and Perko. In the paper their results are extended to the Elliptic problem and applied to prove the existence of second-species solutions generated by rectilinear ellipses in the Circular problem and nearly-rectilinear ones in the Elliptic case. 相似文献