共查询到20条相似文献，搜索用时 31 毫秒
1.
We consider the modified restricted three body problem with power-law density profile of disk, which rotates around the center
of mass of the system with perturbed mean motion. Using analytical and numerical methods, we have found equilibrium points
and examined their linear stability. We have also found the zero velocity surface for the present model. In addition to five
equilibrium points there exists a new equilibrium point on the line joining the two primaries. It is found that L
1 and L
3 are stable for some values of inner and outer radius of the disk while other collinear points are unstable, but L
4 is conditionally stable for mass ratio less than that of Routh’s critical value. Lastly, we have studied the effects of radiation
pressure, oblateness and mass of the disk on the motion and stability of equilibrium points. 相似文献
2.
We have studied the stability of location of various equilibrium points of a passive micron size particle in the field of
radiating binary stellar system within the framework of circular restricted three body problem. Influence of radial radiation
pressure and Poynting-Robertson drag (PR-drag) on the equilibrium points and their stability in the binary stellar systems
RW-Monocerotis and Krüger-60 has been studied. It is shown that both collinear and off axis equilibrium points are linearly unstable for increasing value
of β
1 (ratio of radiation to gravitational force of the massive component) in presence of PR-drag for the binary systems. Further
we find that out of plane equilibrium points (L
i
, i=6,7) may exists for range of values of β
1>1 for these binary systems in the presence of PR-drag. Our linear stability analysis shows that the motion near the equilibrium
points L
6,7 of the binary systems is unstable both in the absence and presence of PR-drag. 相似文献
3.
K. E. Papadakis 《Astrophysics and Space Science》2009,323(3):261-272
In this paper we study the asymptotic solutions of the (N+1)-body ring planar problem, N of which are finite and ν=N−1 are moving in circular orbits around their center of masses, while the Nth+1 body is infinitesimal. ν of the primaries have equal masses m and the Nth most-massive primary, with m
0=β
m, is located at the origin of the system. We found the invariant unstable and stable manifolds around hyperbolic Lyapunov
periodic orbits, which emanate from the collinear equilibrium points L
1 and L
2. We construct numerically, from the intersection points of the appropriate Poincaré cuts, homoclinic symmetric asymptotic
orbits around these Lyapunov periodic orbits. There are families of symmetric simple-periodic orbits which contain as terminal
points asymptotic orbits which intersect the x-axis perpendicularly and tend asymptotically to equilibrium points of the problem spiraling into (and out of) these points.
All these families, for a fixed value of the mass parameter β=2, are found and presented. The eighteen (more geometrically simple) families and the corresponding eighteen terminating
homo- and heteroclinic symmetric asymptotic orbits are illustrated. The stability of these families is computed and also presented. 相似文献
4.
The existence and stability of a test particle around the equilibrium points in the restricted three-body problem is generalized
to include the effect of variations in oblateness of the first primary, small perturbations ϵ and ϵ′ given in the Coriolis and centrifugal forces α and β respectively, and radiation pressure of the second primary; in the case when the primaries vary their masses with time in
accordance with the combined Meshcherskii law. For the autonomized system, we use a numerical evidence to compute the positions
of the collinear points L
2κ
, which exist for 0<κ<∞, where κ is a constant of a particular integral of the Gylden-Meshcherskii problem; oblateness of the first primary; radiation pressure
of the second primary; the mass parameter ν and small perturbation in the centrifugal force. Real out of plane equilibrium points exist only for κ>1, provided the abscissae
x < \fracn(k-1)b\xi<\frac{\nu(\kappa-1)}{\beta}. In the case of the triangular points, it is seen that these points exist for ϵ′<κ<∞ and are affected by the oblateness term, radiation pressure and the mass parameter. The linear stability of these equilibrium
points is examined. It is seen that the collinear points L
2κ
are stable for very small κ and the involved parameters, while the out of plane equilibrium points are unstable. The conditional stability of the triangular
points depends on all the system parameters. Further, it is seen in the case of the triangular points, that the stabilizing
or destabilizing behavior of the oblateness coefficient is controlled by κ, while those of the small perturbations depends on κ and whether these perturbations are positive or negative. However, the destabilizing behavior of the radiation pressure remains
unaltered but grows weak or strong with increase or decrease in κ. This study reveals that oblateness coefficient can exhibit a stabilizing tendency in a certain range of κ, as against the findings of the RTBP with constant masses. Interestingly, in the region of stable motion, these parameters
are void for
k = \frac43\kappa=\frac{4}{3}. The decrease, increase or non existence in the region of stability of the triangular points depends on κ, oblateness of the first primary, small perturbations and the radiation pressure of the second body, as it is seen that the
increasing region of stability becomes decreasing, while the decreasing region becomes increasing due to the inclusion of
oblateness of the first primary. 相似文献
5.
Cédric Langbort 《Celestial Mechanics and Dynamical Astronomy》2002,84(4):369-385
In this paper, we study circular orbits of the J
2 problem that are confined to constant-z planes. They correspond to fixed points of the dynamics in a meridian plane. It turns out that, in the case of a prolate body, such orbits can exist that are not equatorial and branch from the equatorial one through a saddle-center bifurcation. A closed-form parametrization of these branching solutions is given and the bifurcation is studied in detail. We show both theoretically and numerically that, close to the bifurcation point, quasi-periodic orbits are created, along with two families of reversible orbits that are homoclinic to each one of them. 相似文献
6.
Elbaz I. Abouelmagd 《Astrophysics and Space Science》2012,342(1):45-53
In this paper, we prove that the locations of the triangular points and their linear stability are affected by the oblateness of the more massive primary in the planar circular restricted three-body problem, considering the effect of oblateness for J 2 and J 4. After that, we show that the triangular points are stable for 0<μ<μ c and unstable when , where μ c is the critical mass parameter which depends on the coefficients of oblateness. On the other hand, we produce some numerical values for the positions of the triangular points, μ and μ c using planets systems in our solar system which emphasis that the range of stability will decrease; however this range sometimes is not affected by the existence of J 4 for some planets systems as in Earth–Moon, Saturn–Phoebe and Uranus–Caliban systems. 相似文献
7.
On the stabilization of the collinear libration points of the restricted circular three-body problem
The possibility of stabilizing the collinear libration points of the circular restricted three-body problem by using an additional jet acceleration (constant in magnitude) is investigated. Three stabilization laws are considered when the jet acceleration is either directed continuously to one of the primariesm
1,m
2 or is parallel to the line joining them. The solution of the problem formulated is based on the method of the driving forces structure analysis created by W. Thomson and P. Tait. It is shown that none of the stabilization laws mentioned ensures the existence of the isolated minimum of changed potential energy, and therefore the secular stability of the collinear libration points is impossible. In the 3rd and 4th paragraphs the possibility of a gyroscopic stabilization of these points is considered. It is shown that the gyroscopic stabilization of the external libration points is possible only when jet acceleration is either directed to the distant mass or is parallel to the line joining the primaries. The necessary and sufficient conditions of the gyroscopic stabilization are given. It is also shown that the internal libration points cannot be stabilized by any of the laws considered. For the Earth-Moon system the numerical data of time-existence of the satellite in the vicinity of the libration point situated near the Moon are given. 相似文献
8.
We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L
1 and L
2 in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth
system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points
inside L
1 and beyond L
2 where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial
halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion
systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum
amplitude of halo orbits about artificial equilibrium points inside L
1 decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L
2 in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first
increases and then decreases after the thrust acceleration exceeds 0.415 mm/s2. Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times
and require a reasonably small low-thrust acceleration 0.0593 mm/s2. 相似文献
9.
In this paper, we study the existence of libration points and their linear stability when the three participating bodies are axisymmetric and the primaries are radiating, we found that the collinear points remain unstable, it is further seen that the triangular points are stable for 0<μ<μ c , and unstable for where , it is also observed that for these points the range of stability will decrease. In addition to this we have studied periodic orbits around these points in the range 0<μ<μ c , we found that these orbits are elliptical; the frequencies of long and short orbits of the periodic motion are affected by the terms which involve parameters that characterize the oblateness and radiation repulsive forces. The implication is that the period of long periodic orbits adjusts with the change in its frequency while the period of short periodic orbit will decrease. 相似文献
10.
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
11.
We have analysed X-ray spectra of 13 solar flares as obtained by the Bent Crystal Spectrometer (BCS) on the Solar Maximum Mission. In particular, we have examined the observed ratio of T
Fe/T
Ca where T
Fe and T
Ca are the temperatures obtained from the Fexxv and Caxix spectra, respectively. In order to simplify the investigation we have analysed only flares which reach quasi-steady-state during the decay. It turned out that the observed ratios cannot be explained by a model consisting of a single, uniformly heated loop, with a constant or variable cross-sectional area. We propose that this problem may be solved by introducing some distribution of the heating function across the flaring loop. This model has been tested by detailed calculations. 相似文献
12.
This paper focuses on some aspects of the motion of a small particle moving near the Lagrangian points of the Earth–Moon system.
The model for the motion of the particle is the so-called bicircular problem (BCP), that includes the effect of Earth and
Moon as in the spatial restricted three body problem (RTBP), plus the effect of the Sun as a periodic time-dependent perturbation
of the RTBP. Due to this periodic forcing coming from the Sun, the Lagrangian points are no longer equilibrium solutions for
the BCP. On the other hand, the BCP has three periodic orbits (with the same period as the forcing) that can be seen as the
dynamical equivalent of the Lagrangian points. In this work, we first discuss some numerical methods for the accurate computation
of quasi-periodic solutions, and then we apply them to the BCP to obtain families of 2-D tori in an extended neighbourhood
of the Lagrangian points. These families start on the three periodic orbits mentioned above and they are continued in the
vertical (z and ż) direction up to a high distance. These (Cantor) families can be seen as the continuation, into the BCP, of the Lyapunov
family of periodic orbits of the Lagrangian points that goes in the (z, ż) direction. These results are used in a forthcoming work [9] to find regions where trajectories remain confined for a
very long time. It is remarkable that these regions seem to persist in the real system.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
K. E. Papadakis 《Astrophysics and Space Science》2006,302(1-4):67-82
We study numerically the asymptotic homoclinic and heteroclinic orbits around the hyperbolic Lyapunov periodic orbits which
emanate from Euler's critical points L
1 and L
2, in the photogravitational restricted plane circular three-body problem. The invariant stable-unstable manifolds associated
to these Lyapunov orbits, are also presented. Poincaré surface of sections of these manifolds on appropriate planes and several
homoclinic and heteroclinic orbits for the gravitational case as well as for varying radiation factor q
1, are displayed. Homoclinic-homoclinic and homoclinic-heteroclinic-homoclinic chains which link the interior with the exterior
Hill's regions, are illustrated. We adopt the Sun-Jupiter system and assume that only the larger primary radiates. It is found
that for small deviations of its value from the gravitational case (q
1 = 1), the radiation pressure exerts a significant impact on the Hill's regions and on these asymptotic orbits. 相似文献
14.
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
15.
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
16.
K. E. Papadakis 《Astrophysics and Space Science》2006,305(1):57-66
We study numerically the asymptotic homoclinic and heteroclinic orbits associated with the triangular equilibrium points L
4 and L
5, in the gravitational and the photogravitational restricted plane circular three-body problem. The invariant stable-unstable manifolds associated to these critical points, are also presented. Hundreds of asymptotic orbits for equal mass of the primaries and for various values of the radiation pressure are computed and the most interesting of them are illustrated. In the Copenhagen case, which the problem is symmetric with respect to the x- and y-axis, we found and present non-symmetric heteroclinic asymptotic orbits. So pairs of heteroclinic connections (from L
4 to L
5 and vice versa) form non-symmetric heteroclinic cycles. The termination orbits (a combination of two asymptotic orbits) of all the simple families of symmetric periodic orbits, in the Copenhagen case, are illustrated. 相似文献
17.
Due to various perturbations, the collinear libration points of the real Earth–Moon system are not equilibrium points anymore.
Under the assumption that the Moon’s motion is quasi-periodic, special quasi-periodic orbits called dynamical substitutes
exist. These dynamical substitutes replace the geometrical collinear libration points as time-varying equilibrium points.
In the paper, the dynamical substitutes of the three collinear libration points in the real Earth–Moon system are computed.
For the points L
1 and L
2, linearized motions around the dynamical substitutes are described, and the variational equations of the dynamical substitutes
are reduced to a form with a near constant coefficient matrix. Then higher order analytical formulae of the central manifolds
are constructed. Using these analytical solutions as initial seeds, Lissajous orbits and halo orbits are computed with numerical
algorithms. 相似文献
18.
This paper investigates the stability of equilibrium points in the restricted three-body problem, in which the masses of the
luminous primaries vary isotropically in accordance with the unified Meshcherskii law, and their motion takes place within
the framework of the Gylden–Meshcherskii problem. For the autonomized system, it is found that collinear and coplanar points
are unstable, while the triangular points are conditionally stable. It is also observed that, in the triangular case, the
presence of a constant κ, of a particular integral of the Gylden–Meshcherskii problem, makes the destabilizing tendency of the radiation pressures
strong. The stability of equilibrium points varying with time is tested using the Lyapunov Characteristic Numbers (LCN). It
is seen that the range of stability or instability depends on the parameter κ. The motion around the equilibrium points L
i
(i=1,2,…,7) for the restricted three-body problem with variable masses is in general unstable. 相似文献
19.
Thirteen synoptic maps of expansion rate of the coronal magnetic field (CMF; RBR) calculated by the so-called ‘potential model’ are constructed for 13 Carrington rotations from the maximum phase of solar activity cycle 22 through the maximum phase of cycle 23. Similar 13 synoptic maps of solar wind speed (SWS) estimated by interplanetary scintillation observations are constructed for the same 13 Carrington rotations as the ones for the RBR. The correlation diagrams between the RBR and the SWS are plotted with the data of these 13 synoptic maps. It is found that the correlation is negative and high in this time period. It is further found that the linear correlation is improved if the data are classified into two groups by the magnitude of radial component of photospheric magnetic field, |Bphor|; group 1, 0.0 G ≦ |Brpho| < 17.8 G and group 2, 17.8 G ≦ |Brpho|. There exists a strong negative correlation between the RBR and the SWS for the group 1 in contrast with a weak negative correlation for the group 2. Group 1 has a double peak in the density distribution of data points in the correlation diagram; a sharp peak for high-speed solar wind and a low peak for low-speed solar wind. These two peaks are located just on the axis of maximum variance of data points in the correlation diagram. This result suggests that the solar wind consists of two major components and both the high-speed and the low-speed winds emanating from weak photospheric magnetic regions are accelerated by the same mechanism in the course of solar activity cycle. It is also pointed out that the SWS can be estimated by the RBR of group 1 with an empirical formula obtained in this paper during the entire solar activity cycle. 相似文献
20.
This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis
and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that
the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of
equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen
that the triangular points are stable for 0<μ<μ
c
and unstable for
mc ￡ m < \frac12\mu_{c}\le\mu <\frac{1}{2}, where μ
c
is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that
collinear points remain unstable. 相似文献