共查询到20条相似文献，搜索用时 468 毫秒
1.
《New Astronomy》2021
We study the non-collinear libration points in the frame work of photo-gravitational circular restricted three-body problem with Stokes drag acting as a dissipative force and considering the more massive primary as a radiating body and the less massive primary as a triaxial rigid body. The combined effects of radiation pressure and Stokes drag on the existence and stability of non-collinear libration points is analyzed. It is found that there exist two non-collinear libration points and are asymptotically stable in the interval 0.6149 ≤ q ≤ 1 for μ = 0.01, where q and μ are the radiation factor and mass ratio, respectively. 相似文献
2.
We study numerically the photogravitational version of the problem of four bodies, where an infinitesimal particle is moving under the Newtonian gravitational attraction of three bodies which are finite, moving in circles around their center of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle. The fourth body does not affect the motion of the three bodies (primaries). We consider that the primary body m 1 is dominant and is a source of radiation while the other two small primaries m 2 and m 3 are equal. In this case (photogravitational) we examine the linear stability of the Lagrange triangle solution. The allowed regions of motion as determined by the zero-velocity surface and corresponding equipotential curves, as well as the positions of the equilibrium points on the orbital plane are given. The existence and the number of the collinear and the non-collinear equilibrium points of the problem depends on the mass parameters of the primaries and the radiation factor q 1. Critical masses m 3 and radiation q 1 associated with the existence and the number of the equilibrium points are given. The stability of the relative equilibrium solutions in all cases are also studied. In the last section we investigate the existence and location of the out of orbital plane equilibrium points of the problem. We found that such critical points exist. These points lie in the (x,z) plane in symmetrical positions with respect to (x,y) plane. The stability of these points are also examined. 相似文献
3.
This paper deals with the existence and stability of the non-collinear libration points in the restricted three-body problem when both the primaries are ellipsoid with equal mass and identical in shape. We have determined the equations of motion of the infinitesimal mass which involves elliptic integrals and then we have investigated the existence and stability of the non-collinear libration points. This is observed that the non-collinear libration points exist only in the interval 52°<φ<90° and form an isosceles triangle with the primaries. Further we observed that the non collinear libration points are unstable in 52°<φ<90°. 相似文献
4.
C. N. Douskos 《Astrophysics and Space Science》2011,333(1):79-87
Paper presents a complete discussion of the existence, location and stability of the equilibrium points of the coplanar restricted
three-body problem with equal prolate and radiating primaries. Depending on the values of the radiation and negative oblateness
parameters, two or four additional collinear equilibrium points exist, in addition to the three Eulerian points of the classical
case, making up a total of up to seven collinear points. Four of these additional points, as well as the classical central
equilibrium point located at the origin, are stable for certain ranges of the parameters. Also, depending on the values of
the parameters, up to six additional non-collinear equilibrium points exist, in addition to the triangular Lagrangian points
of the classical case. Two of these additional points are located symmetrically above and below the origin and are stable,
while the other four are located symmetrically in the four quadrants and are unstable. 相似文献
5.
This paper studies the motion of an infinitesimal mass around triangular equilibrium points in the elliptic restricted three body problem assuming bigger primary as a source of radiation and the smaller one a triaxial rigid body. A practical application of this case could be the study of motion of a satellite under the effect of Sun and Earth. We have exploited the method of averaging used by Grebnikov (Nauka, Moscow, revised 1986) throughout the analysis of stability of the system. The critical mass ratio depends on the radiation pressure, oblateness, eccentricity and semi major axis of the elliptic orbits and the range of stability decreases as the radiation parameter increases. 相似文献
6.
The linear stability of the triangular equilibrium points in the photogravitational elliptic restricted problem is examined and the stability regions are determined in the space of the parameters of mass, eccentricity, and radiation pressure. It is found that radiation pressure of the larger body for solar system cases exerts only a small quantitative influence on the stability regions. 相似文献
7.
We locate and examine the stability of the ‘out of plane’ equilibrium points, L 6,7 of an infinitesimal body in the field of stellar-oblate binary systems moving in elliptic orbits around their common center of mass. Their positions and stability depend on the oblateness as well as radiation coefficients of the primaries and the eccentricity of their orbits. A numerical application of this problem for the systems: Gamma Leporis and Altair are given. 相似文献
8.
This paper investigates the stability of triangular equilibrium points (L 4,5) in the elliptic restricted three-body problem (ER3BP), when both oblate primaries emit light energy simultaneously. The positions of the triangular points are seen to shift away from the line joining the primaries than in the classical case on account of the introduction of the eccentricity, semi-major axis, radiation and oblateness factors of both primaries. This is shown for the binary systems Achird, Luyten 726-8, Kruger 60, Alpha Centauri AB and Xi Bootis. We found that motion around these points is conditionally stable with respect to the parameters involved in the system dynamics. The region of stability increases and decreases with variability in eccentricity, oblateness and radiation pressures. 相似文献
9.
Badam Singh Kushvah 《Astrophysics and Space Science》2008,318(1-2):41-50
The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh’s problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The effect of radiation pressure has been discussed numerically. The collinear points are linearly unstable and triangular points are stable in the sense of Lyapunov stability provided μ<μ Routh =0.0385201. The effect of gravitational potential from the belt is also examined. The mathematical properties of this system are different from the classical restricted three body problem. 相似文献
10.
This paper deals with the existence and the stability of the libration points in the restricted three-body problem when the smaller primary is an ellipsoid. We have determined the equations of motion of the infinitesimal mass which involves elliptic integrals and then we have investigated the collinear and non collinear libration points and their stability. This is observed that there exist five collinear libration points and the non collinear libration points are lying on the arc of the unit circle whose centre is the bigger primary. Further observed that the libration points either collinear or non-collinear all are unstable. 相似文献
11.
12.
《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
13.
Jagadish Singh 《Astrophysics and Space Science》2012,342(2):303-308
This paper studies the motion of an infinitesimal body near the out-of-plane equilibrium points, L 6,7, in the perturbed restricted three-body problem. The problem is perturbed in the sense that the primaries of the system are oblate spheroids as well as sources of radiation and small perturbations are give to the Coriolis and centrifugal forces. It locates the positions and examines the stability of L 6,7 with a particular application to the binary system Struve 2398. It is observed that their positions are affected by the radiation, oblateness and a small perturbation in the centrifugal force, but is unaffected by that of the Coriolis force. They are also found to be unstable. 相似文献
14.
This paper studies the stability of infinitesimal motions about the triangular equilibrium points in the elliptic restricted three body problem assuming bigger primary as a source of radiation and the smaller one a triaxial rigid body. The perturbation technique developed by Bennet (Icarus 4:177, 1965b) has been used for determination of characteristic exponents. This technique is based on Floquet’s Theory for determination of characteristic exponents in the system with periodic coefficients. The results of the study are analytical and numerical expressions are simulated for the transition curves bounding the region of stability in the μ–e plane, accurate to O(e 2). The unstable region is found to be divided into three parts. The effect of radiation parameter is significant. For small values of e, the results are in favor with the numerical analysis of Danby (Astron. J. 69:166, 1964), Bennet (Icarus 4:177, 1965b), Alfriend and Rand (AIAA J. 6:1024, 1969). The effect of radiation pressure is significant than the oblateness and triaxiality of the primaries. 相似文献
15.
In this paper, we extend the basic model of the restricted four-body problem introducing two bigger dominant primaries m 1 and m 2 as oblate spheroids when masses of the two primary bodies (m 2 and m 3) are equal. The aim of this study is to investigate the use of zero velocity surfaces and the Poincaré surfaces of section to determine the possible allowed boundary regions and the stability orbit of the equilibrium points. According to different values of Jacobi constant C, we can determine boundary region where the particle can move in possible permitted zones. The stability regions of the equilibrium points expanded due to presence of oblateness coefficient and various values of C, whereas for certain range of t (100≤t≤200), orbits form a shape of cote’s spiral. For different values of oblateness parameters A 1 (0<A 1<1) and A 2 (0<A 2<1), we obtain two collinear and six non-collinear equilibrium points. The non-collinear equilibrium points are stable when the mass parameter μ lies in the interval (0.0190637,0.647603). However, basins of attraction are constructed with the help of Newton Raphson method to demonstrate the convergence as well as divergence region of the equilibrium points. The nature of basins of attraction of the equilibrium points are less effected in presence and absence of oblateness coefficients A 1 and A 2 respectively in the proposed model. 相似文献
16.
The restricted three body problem is generalised to include the effects of an inverse square distance radiation pressure force
on the infinitesimal mass due to the primaries, which are both radiating. In this paper we investigate the stability of out-of-plane
equilibrium points, based on equations in variations. We have found the characteristic equation for the complex normal frequencies
which is a sixth order polynomial. Thus we conclude that out-of-plane equilibrium points are unstable due to positive real
part in complex roots. 相似文献
17.
Generoso Aliasi Giovanni Mengali Alessandro A. Quarta 《Celestial Mechanics and Dynamical Astronomy》2012,114(1-2):181-200
Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory. 相似文献
18.
The linear stability of the triangular equilibrium points in the photogravitational elliptic restricted three-body problem is examined and the stability regions are determined in the space of the parameters of mass, eccentricity, and radiation pressure, in the case of equal radiation factors of the two primaries. The full range of values of the common radiation factor is explored, from the gravitational caseq
1 =q
2 =q = 1 down to the critical value ofq = 1/8 at which the triangular equilibria disappear by coalescing on the rotating axis of the primaries. It is found that radiation pressure exerts a significant influence on the stability regions. For certain intervals of radiation values these regions become qualitatively different from the gravitational case as well as the solar system case considered in Paper I. There exist values of the common radiation factor, in the range considered, for which the triangular equilibrium points are stable for the entire range of mass distribution among the primaries and for large eccentricities of their orbits. 相似文献
19.
Ashraf Hamdy Mostafa K. Ahmed Mohamad Radwan Fawzy Ahmed Abd El-Salam 《Earth, Moon, and Planets》2003,93(4):261-273
The objective of the present work is to develope explicit analytical expressions for the small amplitude orbits of the infinitesimal
mass about the equilibrium points in the elliptic restricted three body problem. To handle this dynamical problem, the Hamiltonian
for the elliptic problem is formed with the true anomaly and then with the eccentric anomaly as independent variables. The
origin is then transformed to a fixed point and the Hamiltonian is developed up to O(4) in the eccentricity, e, (which plays the role of the small parameter of the problem) of the primaries. The integration of the model problem under
consideration is undertaken by means of a perturbation technique based on Lie series developments, which leads to the solution
of the canonical equations of motion. 相似文献
20.
R. K. Choudhry 《Celestial Mechanics and Dynamical Astronomy》1977,16(4):411-419
In this paper the existence of collinear as well as equilateral libration points for the generalised elliptic restricted three body problem has been studied distinct from Kondurar and Shinkarik (1972) where a study has been made for the generalised circular restricted three body problem. Here the coordinates of the libration points have been found to be functions of timet. 相似文献