首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 343 毫秒
1.
The non-linear stability of the triangular libration point L4 of the restricted three-body problem is studied under the presence of third- and fourth-order resonances, when the more massive primary is a triaxial rigid body and source of radiation. In this study, Markeev's theorems are applied with the help of Moser's theorem. It is found that the stability of the triangular libration point is unstable in the third-order resonance case and in the fourth-order resonance case, this is stable or unstable depending on A1 and A2, and a source of radiation parameter α, where A1, A2 depend upon the lengths of the semi-axes of the triaxial rigid body.  相似文献   

2.
This paper considers the restricted circular three-body problem with respect to the radiation repulsion force acting upon a particle on the part of one of the main bodies (the Sun). The characteristic of the family of stationary particular solutions of the problem (libration points) representing the relative equilibrium positions in a rotating Cartesian system is given. On the basis of the KAM theory with the help of a computer a nonlinear analysis of the triangular libration points stability for the planar case is carried out. These libration points are proved to be strictly stable by Liapunov practically in the whole area of fulfilling the necessary stability conditions. Instability is discovered at the resonant curve of the third order and at the greater part of the resonant curve of the fourth order. The plotted results of the investigation allowed us to draw a conclusion about the Liapunov stability of the triangular libration points in a problem with respect to the radiation pressure for all the planets of the Solar system.  相似文献   

3.
The stability of collinear and triangular libration points is investigated in the photogravitational elliptic restricted three-body problem, in which two primary bodies emit light energy simultaneously. The conditions of stability of the collinear and triangular libration points are obtained based on a linearized set of equations of perturbed motion for various values of the eccentricity of the Keplerian orbits and the mass ratio of the primary bodies. The maximal numerical value is defined for the eccentricity at which a stable libration point can still exist. It is demonstrated how the parametric resonance causes an instability of collinear and triangular libration points; the evolution of the origination of the instability zones is traced. The minimal eccentricity value is found at which zones of instability of triangular libration points arise.  相似文献   

4.
Out-of-plane motion about libration points is studied within the framework of the elliptic restricted three-body problem. Nonlinear motion in the circular restricted problem is given to third order in the out-of-plane amplitudeA z by Jacobi elliptic functions. Linear motion in the elliptic problem is studied using Mathieu's and Hill's equations. Additional terms needed for a complete third-order theory are found using Lindsted's method. This theory is constructed for the case of collinear libration points; for the case of triangular points, a third-order nonlinear solution is given separately in terms of Jacobi elliptic functions.  相似文献   

5.
This paper investigates the triangular libration points in the photogravitational restricted three-body problem of variable mass, in which both the attracting bodies are radiating as well and the infinitesimal body vary its mass with time according to Jeans’ law. Firstly, applying the space-time transformation of Meshcherskii in the special case when q=1/2, k=0, n=1, the differential equations of motion of the problem are given. Secondly, in analogy to corresponding problem with constant mass, the positions of analogous triangular libration points are obtained, and the fact that these triangular libration points cease to be classical ones when α≠0, but turn to classical L 4 and L 5 naturally when α=0 is pointed out. Lastly, introducing the space-time inverse transformation of Meshcherskii, the linear stability of triangular libration points is tested when α>0. It is seen that the motion around the triangular libration points become unstable in general when the problem with constant mass evolves into the problem with decreasing mass.  相似文献   

6.
We study the fourth-order stability of the triangular libration points in the absence of resonance for the three-body problem when the infinitesimal mass is affected not only by gravitation but also by light pressure from both primaries. A comprehensive summary of previous results is given, with some inaccuracies being corrected. The Lie triangle method is used to obtain the fourth-order Birkhoff normal form of the Hamiltonian, and the corresponding complex transformation to pre-normal form is given explicitly. We obtain an explicit expression for the determinant required by the Arnold-Moser theorem, and show that it is a rational function of the parameters, whose numerator is a fifth-order polynomial in the mass parameter. Particular cases where this polynomial reduces to a quartic are described. Our results reduce correctly to the purely gravitational case in the appropriate limits, and extend numerical work by previous authors.  相似文献   

7.
In this paper we have examined the stability of triangular libration points in the restricted problem of three bodies when the bigger primary is an oblate spheroid. Here we followed the time limit and computational process of Tuckness (Celest. Mech. Dyn. Mech. 61, 1–19, 1995) on the stability criteria given by McKenzie and Szebehely (Celest. Mech. 23, 223–229, 1981). In this study it was found that in comparison to other studies the value of the critical mass μ c has been reduced due to oblateness of the bigger primary, i.e. the range of stability of the equilateral triangular libration points reduced with the increase of the oblateness parameter I and hence the order of commensurability was increased.  相似文献   

8.
The stability of the triangular libration points in the case when the first and the second order resonances appear was investigated. It was proved that the first order resonances do not cause instability. The second order resonances may lead to instability. Domains of the instability in the two-dimensional parameter space were determined.  相似文献   

9.
In a recent paper, published in Astrophys. Space Sci. (337:107, 2012) (hereafter paper ZZX) and entitled “On the triangular libration points in photogravitational restricted three-body problem with variable mass”, the authors study the location and stability of the generalized Lagrange libration points L 4 and L 5. However their study is flawed in two aspects. First they fail to write correctly the equations of motion of the variable mass problem. Second they attribute a variable mass to the third body of the restricted three-body model, a fact that is not compatible with the assumptions used in deriving the mathematical formulation of this model.  相似文献   

10.
A number of criteria for linear stability of libration points in the perturbed restricted three-body problem are presented. The criteria involve only the coefficients of the characteristic equation of the tangent map of the libration points and can be easily applied. With these criteria the effect of drag on the linear stability of the triangular libration points in the classical restricted three-body problem is investigated. Some of Murray et al.'s results are improved.  相似文献   

11.
The configuration space around the triangular libration points in the Earth-Moon system is partitioned according to the stability of the motion. The regions aroundL 4 andL 5 are established where particles placed with zero initial velocity will librate. The complexity of the partitioning is revealed.  相似文献   

12.
We present a geometric interpretation of the spectral stability of the triangular libration points in the charged three-body problem. We obtain that the spectral stability varies with the position of the center of mass of the three charges with respect to the circumcenter of the triangle configuration, which does not depend directly of the charges. If the center of mass is outside or on the circumference of a well defined radius ??, then spectral stability occurs. In addition, we analyze the existence of resonances within the spectral region of stability under this geometric interpretation, determining resonance curves of order 2, 3, 4, . . ., some of them with multiple resonances.  相似文献   

13.
In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

14.
Within the frame work of the circular restricted three-body problem (CR3BP) we have examined the effect of axis-symmetric of the bigger primary, oblateness up to the zonal harmonic J 4 of the smaller primary and gravitational potential from a belt (circular cluster of material points) on the linear stability of the triangular libration points. It is found that the positions of triangular libration points and their linear stability are affected by axis-symmetric of the bigger primary, oblateness up to J 4 of the smaller primary and the potential created by the belt. The axis-symmetric of the bigger primary and the coefficient J 2 of the smaller primary have destabilizing tendency, while the coefficient J 4 of the smaller primary and the potential from the belt have stabilizing tendency. The overall effect of these perturbations has destabilizing tendency. This study can be useful in the investigation of motion of a particle near axis-symmetric—oblate bodies surrounded by a belt.  相似文献   

15.
We investigate the stability of the triangular libration points when both the attracting bodies are radiating under the resonance conditions 1 = 22 and 32.  相似文献   

16.
Third and fourth order mean motion resonances are studied in the model of the restricted three-body problem by numerical methods for mass parameters corresponding approximately to the Sun?CJupiter and Sun?CNeptune systems. In the case of inner resonances, it is shown that there are two regions of libration in the 8:5 and 7:4 resonances, one at low, the other at high eccentricities. In the 9:5 and 7:3 resonances libration can exist only in one region at high eccentricities. The 5:2 and 4:1 resonances are very regular, with one librational zone existing for all eccentricities. There is no visible region of libration at any eccentricities in the 5:1 resonance, the transition between the regions of direct and retrograde circulation is very sharp. In the case of outer resonances, the 8:5 and 7:4 resonances have also two regions of libration, but the 9:5 resonance has three, the 7:3 resonance two librational zones. The 5:2 resonance is again very regular, but it is parted for two regions of libration at high eccentricities. Libration is possible in the 4:1 resonance only at high eccentricities. The 5:1 resonance is very symmetric. In the case of outer resonances, a comparison is made with trans-Neptunian objects (TNO) in higher order mean motion resonances. Several new librating TNOs are identified.  相似文献   

17.
The restricted three-body problem is generalized with the inclusion of solar radiation pressure. For small particles (typically 1 m to 1 mm) the familiar equilibrium triangular points L4 and L5 no longer exist. However libration orbits are not completely destroyed, although an effect of resonance causes their amplitude to be very large, for a particle initially at rest at either of the triangular point. Finally the results of a study of the linearized equations of motion, supplemented by a numerical integration, rule out the possibility of an accumulation of dust at the Earth-Moon lagrangian triangular points.  相似文献   

18.
We consider the motion of a test particle around a triaxial primary and an oblate companion orbiting each other in elliptic orbits about their common barycenter in the neighborhood of triangular libration points. The positions and stability of these points are influenced by the triaxiality and oblateness of the primary and secondary, and by the semi-major axis and eccentricity of the orbits. The triangular points are stable for 0<μ<μ c ; where μ is the mass ratio (μ≤1/2) and μ c is the critical mass value influenced by the eccentricity, oblateness, semi major axis and triaxiality factors. The size of the region of stability increases with decreasing values of triaxiality and oblateness. An application of the results obtain to double neutron star binaries results show that the positions and stability of the triangular points of PSR J1518+4904, PSR B1534+12, PSR B1914+16 and PSR B2127+11c are affected by the parameters in the systems’ dynamics.  相似文献   

19.
H.J. Reitsema 《Icarus》1981,48(1):140-142
The 1980 observations of the Saturn system have revealed objects at both the preceding (L4) and following (L5) triangular libration points of Tethys (S4). The observations indicate a small (～2°) libration amplitude for the L4 body while the data on the L5 object are insufficient to define its libration amplitude.  相似文献   

20.
The main aim of this paper is to study the existence of resonance and linear stability of the triangular equilibrium points of the planar elliptical restricted three body problem considering the photo gravitational effect of both the primaries in circular and elliptical case. A practical application of this case could be the study of the dynamical system around the binary systems. For this the Hamiltonian function, convergent in nature and describing the motion of the infinitesimal body in the neighborhood of the triangular equilibrium solutions is derived. Also, the Hamiltonian for the system is expanded in powers of the generalized components of momenta. Further, canonical transformation has also been used to study the stability of the triangular equilibrium points. The study primarily focuses on establishing the relation for determining the range of stability at and near the resonance frequency ω 2=1/2 around the binary systems using simulation technique. It is observed that the parametric resonance is only possible at the resonance frequency ω 2=1/2 in both circular and elliptical cases.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号