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1.
The paper deals with a simple photo-gravitational model of N+1 bodies. The motion of a small particle which subjects both
the gravitational attraction and the radiation pressure is studied in a regular polygon configuration of N bodies. The dynamical
features of this model are investigated for a wide range of values of the radiation parameters by mapping its equilibrium
points and periodic orbits. The results show that for these values, radiation merely affects quantitatively the characteristics
of the system, while it leaves unaffected the stability of the particle periodic motions and equilibria.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Tilemahos J. Kalvouridis 《Celestial Mechanics and Dynamical Astronomy》2008,102(1-3):191-206
The focus of this contribution is an effort to review and report the main results obtained so far, concerning the periodic motions of a small body in the combined gravitational field created by a regular ν-gon arrangement of ν big bodies with equal masses, where ν > 7, and another central primary with different mass. Various types of planar periodic motions are presented and networks of characteristic curves of families are depicted, in order to show their distribution in the space of the initial conditions, as well as the evolution of their members that are also examined under the variation of the parameters of the system. Furthermore, the regions of the allowed three-dimensional motions, as well as their variation, are illustrated by means of the zero-velocity surfaces. All this new material is added to the already existing data, and completes thus the profile of the dynamical behavior of the system. 相似文献
3.
Periodic Solutions in the Ring Problem 总被引：3，自引：0，他引：3
T.J. Kalvouridis 《Astrophysics and Space Science》1999,266(4):467-494
In this article we investigate the symmetric periodic motions of a particle of negligible mass in a coplanar N-body system
consisting of ν=N-1 peripheral equidistant bodies of equal masses and a central body with a different mass. This system which
we refer to as the ring problem, is a simple model approximating the planar problem of N bodies.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
The photo-gravitational problems of two or more bodies have attracted much attention during the last decades. In this paper, radiation is considered as an additional factor influencing the particle motion in a regular polygon formation of N big bodies where the ν = Ν ? 1 primary bodies have equal masses and are located at the vertices of a regular polygon and the Nth primary has different mass and is located at the mass center of the system. We assume that some or all the primary bodies are radiation sources and we numerically explore various cases where symmetry of the resultant force field with respect to the same axis is preserved. For the purposes of our investigation we adopt Radzievski’s theory and assumptions. The material gathered helps us to estimate the radiation effect on the evolution of periodic orbits and their characteristics, such as their periods and their stability. Figures and diagrams illustrate these alterations and document our conclusions. 相似文献
5.
Parameters play a very important and determinative role in the dynamics of a dynamical system as well as in the formation
of its particular characteristics. In this paper we investigate the way in which a large scale variation of the mass parameter,
influences the behavior of a mass-less particle which moves in the vicinity of a ring arrangement of N-bodies. More precisely, we study the impact of this parameter on periodic motions and their characteristics. 相似文献
6.
The study of a dynamical system comprises a variety of processes, each one of which requires careful analysis. A fundamental preliminary step is to detect and limit the regions where solutions may exist. In the case of the ring problem of (N+1)-bodies or, otherwise, the regular polygon problem of (N+1) bodies, the existence of a Jacobian-type integral of motion constitutes the key for the investigation of the areas where the motions of the small particle are realized. Based on the aforementioned integral, we present an extended study of the parametric evolution of the regions where 3-D particle motions may exist. 相似文献
7.
Vladislav V. Sidorenko 《Celestial Mechanics and Dynamical Astronomy》2011,109(4):367-384
This paper is devoted to the special case of the restricted circular three-body problem, when the two primaries are of equal
mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the
primaries (so called periodic vertical motions). The main goal of the paper is to study the stability of these periodic motions
in the linear approximation. A special attention is given to the alternation of stability and instability within the family
of periodic vertical motions, whenever their amplitude is varied in a continuous monotone manner. 相似文献
8.
Gastón Beltritti Fernando Mazzone Martina Oviedo 《Celestial Mechanics and Dynamical Astronomy》2018,130(7):45
In this paper we address an \(n+1\)-body gravitational problem governed by the Newton’s laws, where n primary bodies orbit on a plane \(\varPi \) and an additional massless particle moves on the perpendicular line to \(\varPi \) passing through the center of mass of the primary bodies. We find a condition for the described configuration to be possible. In the case when the primaries are in a rigid motion, we classify all the motions of the massless particle. We study the situation when the massless particle has a periodic motion with the same minimal period as the primary bodies. We show that this fact is related to the existence of a certain pyramidal central configuration. 相似文献
9.
《New Astronomy》2020
We consider the square configuration of photo-gravitational elliptic restricted five-body problem and study the Sitnikov motions. The four radiating primaries are of equal mass placed at the vertices of square and the fifth body having negligible mass performs oscillations along a straight line perpendicular to the orbital plane of the primaries. The motion of the fifth body is called vertical periodic motion and the main aim of this paper is to study the effect of radiation pressure on these periodic motions in the linear approximation. Moreover, the effects of radiation pressure on the motion of fifth body have been examined with the help of Poincare surfaces of section. By escalating the radiation pressure, surrounding periodic tubes and islands disappear and chaotic motion occurs near the hyperbolic points. Further, by escalating the radiation pressure, the main stochastic region joins the escaping one. 相似文献
10.
Haibin Shang Xiaoyu Wu Pingyuan Cui 《Celestial Mechanics and Dynamical Astronomy》2017,127(2):185-210
Ground observations have found that asynchronous systems constitute most of the population of the near-Earth binary asteroids. This paper concerns the trajectory of a particle in the asynchronous system which is systematically described using periodic ellipsoidal and spherical body models. Due to the non-autonomous characteristics of the asynchronous system, Lagrangian coherent structures (LCS) are employed to identify the various dynamical behaviors. To enhance the accuracy of LCS, a robust LCS finding algorithm is developed incorporating hierarchical grid refinement, one-dimensional search and variational theory verification. In this way, the intricate dynamical transport boundaries are detected efficiently. These boundaries indicate that a total of 15 types of trajectories exist near asynchronous binary asteroids. According to their Kepler energy variations, these trajectories can be grouped into four basic categories, i.e., transitory, escape, impact and flyby trajectories. Furthermore, the influence of the ellipsoid’s spin period on the dynamical behavior is discussed in the context of the change of dynamical regions. We found that the transitory and impact motions occur easily in the synchronous-like binary systems, in which the rotation period of the ellipsoid is nearly equal to that of the mutual orbit. Meanwhile, the results confirm a positive correlation between the spinning rate of the ellipsoid and the probability of the escape and flyby trajectories. The LCS also reveal a marked increase in trajectory diversity after a larger initial energy is selected. 相似文献
11.
We consider the photogravitational restricted three-body problem with oblateness and study the Sitnikov motions. The family of straight line oscillations exists only in the case where the primaries are of equal masses as in the classical Sitnikov problem and have the same oblateness coefficients and radiation factors. A perturbation method based on Floquet theory is applied in order to study the stability of the motion and critical orbits are determined numerically at which families of three-dimensional periodic orbits of the same or double period bifurcate. Many of these families are computed. 相似文献
12.
《New Astronomy》2024
We numerically study a version of the synchronous circular restricted three-body problem, where an infinitesimal mass body is moving under the Newtonian gravitational forces of two massive bodies. The primary body is an oblate spheroid while the secondary is an elongated asteroid of a combination of two equal masses forming a rotating dipole which is synchronous to the rotation of the primaries of the classic circular restricted three-body problem. In this paper, we systematically examine the existence, positions, and linear stability of the equilibrium points for various combinations of the model's parameters. We observe that the perturbing forces have significant effects on the positions and stability of the equilibrium points as well as the regions where the motion of the particle is allowed. The allowed regions of motion as determined by the zero-velocity surface and the corresponding isoenergetic curves as well as the positions of the equilibrium points are given. Finally, we numerically study the binary system Luhman-16 by computing the positions of the equilibria and their stability as well as the allowed regions of motion of the particle. The corresponding families of periodic orbits emanating from the collinear equilibrium points are computed along with their stability properties. 相似文献
13.
We study the simple periodic orbits of a particle that is subject to the gravitational action of the much bigger primary bodies
which form a regular polygonal configuration of (ν+1) bodies when ν=8. We investigate the distribution of the characteristic curves of the families and their evolution in the phase space of
the initial conditions, we describe various types of simple periodic orbits and we study their linear stability. Plots and
tables illustrate the obtained material and reveal many interesting aspects regarding particle dynamics in such a multi-body
system. 相似文献
14.
We study the regions of finite motions in the vicinity of three simple stable periodic orbits in the general problem of three equal-mass bodies with a zero angular momentum. Their distinctive feature is that one of the moving bodies periodically passes through the center of mass of the triple system. We consider the dynamical evolution of plane nonrotating triple systems for which the initial conditions are specified in such a way that one of the bodies is located at the center of mass of the triple system. The initial conditions can then be specified by three parameters: the virial coefficient k and the two angles, φ1 and φ2, that characterize the orientation of the velocity vectors for the bodies. We scanned the region of variation in these parameters k∈(0, 1); φ1, φ2∈(0, π) at steps of δk=0.01; δφ1=δφ2=1° and identified the regions of finite motions surrounding the periodic orbits. These regions are isolated from one another in the space of parameters (k, φ1, φ2). There are bridges that correspond to unstable orbits with long lifetimes between the regions. During the evolution of these metastable systems, the phase trajectory can “stick” to the vicinity of one of the periodic orbits or move from one vicinity to another. The evolution of metastable systems ends with their breakup. 相似文献
15.
In this paper we consider a restricted equilateral four-body problem where a particle of negligible mass is moving under the Newtonian gravitational attraction of three masses (called primaries) which move on circular orbits around their center of masses such that their configuration is always an equilateral triangle (Lagrangian configuration). We consider the case of two bodies of equal masses, which in adimensional units is the parameter of the problem. We study numerically the existence of families of unstable periodic orbits, whose invariant stable and unstable manifolds are responsible for the existence of homoclinic and heteroclinic connections, as well as of transit orbits traveling from and to different regions. We explore, for three different values of the mass parameter, what kind of transits and energy levels exist for which there are orbits with prescribed itineraries visiting the neighborhood of different primaries. 相似文献
16.
A. P. Markeev 《Astronomy Letters》2001,27(7):475-479
The centers of the gaps observed in the asteroid belt are displaced toward Jupiter from their positions that correspond to the exact commensurability between the mean motions of an asteroid and Jupiter. Using the current theory of stability and nonlinear oscillations of Hamiltonian systems, we point out the dynamical causes of this asymmetry. Our analysis is performed in terms of the plane circular restricted three-body problem. The orbits that correspond to Poincaré periodic solutions of the first kind are taken as unperturbed asteroid orbits. 相似文献
17.
Maxwell’s ring-type configuration (i.e. an N-body model where the ν = Ν − 1 bodies have equal masses and are located at the vertices of a regular ν-gon while the N-th body with a different mass is located at the center of mass of the system) has attracted special attention during the
last 15 years and many aspects of it have been studied by considering Newtonian and post-Newtonian potentials (Mioc and Stavinschi
1998, 1999), homographic solutions (Arribas et al.
2007) and relative equilibrium solutions (Elmabsout 1996), etc. An equally interesting problem, known as the ring problem of (N + 1) bodies, deals with the dynamics of a small body in the combined force field produced by such a configuration. This is
the problem we are dealing with in the present paper and our aim is to investigate the variations in the dynamics of the small
body in the case that the central primary is also a radiating source and therefore acts on the particle with both gravitation
and radiation. Based on the general outlines of Radzievskii’s model, we study the permitted and the existing trapping regions
of the particle, its equilibrium locations and their parametric variations as well as the existence of focal points in the
zero-velocity diagrams. The distribution of the characteristic curves of families of planar symmetric periodic orbits and
their stability for various values of the radiation coefficient of the central body is additionally investigated. 相似文献
18.
19.
A family of straight line periodic motions, known as the Sitnikov motions and existing in the case of equal primaries of the three body problem, is studied with respect to stability and bifurcations. Continuation of the bifurcations into the case of unequal primaries is also discussed and some of the bifurcating families of three-dimensional periodic motions are computed. 相似文献
20.
In this paper, families of simple symmetric and non-symmetric periodic orbits in the restricted four-body problem are presented.
Three bodies of masses m
1, m
2 and m
3 (primaries) lie always at the apices of an equilateral triangle, while each moves in circle about the center of mass of the
system fixed at the origin of the coordinate system. A massless fourth body is moving under the Newtonian gravitational attraction
of the primaries. The fourth body does not affect the motion of the three bodies. We investigate the evolution of these families
and we study their linear stability in three cases, i.e. when the three primary bodies are equal, when two primaries are equal
and finally when we have three unequal masses. Series, with respect to the mass m
3, of critical periodic orbits as well as horizontal and vertical-critical periodic orbits of each family and in any case of
the mass parameters are also calculated. 相似文献