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1.
In this paper we prove the existence of ring-type bounded motion in an isolated system consisting of a massive point particle and a homogeneous cube. We study the case of planar motion where the particle moves in a symmetry plane of the cube and we use a rotating frame of reference with its center at the mass center of the cube and its axes coinciding with the symmetry axes of the cube. We prove that, for negative values of the total energy and properly chosen values of the total angular momentum, the relative distance of the bodies has an upper and a lower bound-i.e., the regions of possible motion lie inside an annulus around the cube (motion inside a ring or an island). 相似文献
2.
M. Michalodimitrakis 《Astrophysics and Space Science》1975,37(1):131-142
A quantitative study of periodic orbits and particle trapping near them in the gravitational field of a uniformly rotating homogeneous solid parallelepiped is made. It is found that particle trapping leads to the possibility of formation of ring-like structures around the parallelepiped and blob-like concentrations around the equilibrium points of the parallelepiped. 相似文献
3.
M. Michalodimitrakis 《Astrophysics and Space Science》1981,75(2):289-305
By generalizing the restricted three-body problem, we introduce the restricted four-body problem. We present a numerical study of this problem which includes a study of equilibrium points, regions of possible motion and periodic orbits. Our main motivation for introducing this problem is that it can be used as an intermediate step for a systematic exploration of the genral four-body problem. In an analogous way, one may introduce the restrictedN-body problem. 相似文献
4.
S. Ichtiaroglou K. Katopodis M. Michalodimitrakis 《Astrophysics and Space Science》1980,73(2):445-451
In this paper we present four families of vertical critical periodic orbits found by continuation, with respect to the small massm
3, of the vertical critical periodic orbitsl1v, ilv, mlv, c3v of the circular restricted problem. The periodic orbits refer to a suitably defined rotating frame of reference. 相似文献
5.
S. Ichtiaroglou K. Katopodis Michalodimitrakis 《Journal of Astrophysics and Astronomy》1989,10(4):367-380
Three-dimensional planetary systems are studied, using the model of the restricted three-body problem for Μ =.001. Families
of three-dimensional periodic orbits of relatively low multiplicity are numerically computed at the resonances 3/1, 5/3, 3/5
and 1/3 and their stability is determined. The three-dimensional orbits are found by continuation to the third dimension of
the vertical critical orbits of the corresponding planar problem 相似文献
6.
In this paper we prove the existence of bounded motions for an isolated system consisting of a solid bodyB
1 and a material pointB
2 moving under their mutual gravitational attraction. We also consider the special case where the mass ofB
1 is symmetrically distributed with respect to three mutually perpendicular planes passing through its mass center andB
2 moves on one of these planes. We study the types of the regions of possible motion and the ways of their evolution as the energy or the angular momentum of the system changes. As an example we present some results from a numerical study of the case whereB
1 is a homogeneous prolate spheroid. 相似文献
7.
The energy and the angular momentum integral of motion for the planar three point problem cannot assure bounded motion. In this paper it is shown that if one of the points is replaced by a homogeneous sphere then bounded motion can be found. The zero velocity surfaces for this modified problem are found and their evolution is described. 相似文献
8.
We study the properties of the families of three-dimensional periodic orbits which bifurcate from the vertical critical orbits of the retrograde family of quasi-circular plane periodic orbits which extend from the galactic center up to infinity. We consider the case of a barred galaxy with a strong central bulge. The values of the parameters are chosen in such a way as to cover the cases of a strong or weak bar with a fast or slow rotation. 相似文献
9.
M. Michalodimitrakis 《Astrophysics and Space Science》1978,58(1):125-129
It is proved that the vertical critical orbits of the planar circular restricted three-body problem can be used as starting points for finding periodic orbits of the three-dimensional generalN-body problem. A numerical example is given. 相似文献
10.
In this paper we establish the possibility of a new mechanism for the formation of ring-like structures in barred galaxies. We study the stability of periodic orbits with respect to perturbations perpendicular (vertical stability) or tangent (plane stability) to the plane of motion and we find that matter can be trapped in the case of a relatively strong and fast bar, in a narrow annular region around the bar. The periodic orbits inside the annulus are totally stable—i.e., both vertically and plane. The region outside the annulus is depleted of matter by the action of vertical or plane instability. The resulting ring-like structure has the geometrical characteristics of the true inner rings observed in barred galaxies. In this way the formation of inner rings seems to be a result of combined action ofvertical and plane instability. A similar study of stability in the outer parts of the Galaxy, where outer rings are observed, shows that the above mechanism is absent there. 相似文献