共查询到20条相似文献，搜索用时 64 毫秒
1.
The procedure of numerical ascent from families of planar to three-dimensional periodic orbits and the subsequent descent to the plane is proved efficient in determining new families of planar asymmetric periodic orbits in the restricted three-body problem. Two such families are computed and described for values of the mass parameter for which it has been found that they exist. Two new families of three-dimensional asymmetric periodic orbits are also presented in this paper. 相似文献
2.
P. G. Kazantzis 《Astrophysics and Space Science》1980,69(2):353-368
New families of three-dimensional double-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (
v
= – 1, b
v
– 0) of the basic plane familiesi, g
1, g2, c andI. Further, the predictor-corrector procedure employed to reveal these families has been described and interesting numerical results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. 相似文献
3.
P. G. Kazantzis 《Astrophysics and Space Science》1979,61(2):357-367
Two new families of three-dimensional simple-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families emanate from the vertical-critical orbits (v = 1,c
v
= 0)of the familiesi andl of plane symmetric simpleperiodic orbits direct around the Sun and the Sun-Jupiter respectively. Further, the numerical technique employed in the determination of these families has been described and interesting results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. 相似文献
4.
Formulae containing the elements of the variational matrix are obtained which determine the linear iso-energetic stability parameters of periodic orbits of the general three-body problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The procedure is applied for the determination of horizontally critical orbits among the members of sets of vertical-critical periodic orbits of the threebody problem. These critical-critical orbits have special importance as they delimit the regions in the space of initial conditions which correspond to possibly stable three-dimensional periodic motion of low inclination. 相似文献
5.
C. Zagouras 《Astrophysics and Space Science》1977,50(2):383-407
A number of partly known families of symmetric three-dimensional periodic orbits of the restricted three-body (=0.4) problem are numerically continued in both ends until they terminate with orbits in the plane of motion of the primaries. The families of plane symmetric periodic orbits from which they bifurcate are identified and many orbit illustrations are given. 相似文献
6.
P. G. Kazantzis 《Astrophysics and Space Science》1979,61(2):477-486
Families of three-dimensional axisymmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (v = 1,b
v = 0) of the basic plane familiesi andI. Further the predictor-corrector procedure employed to reveal these families has been described and interesting numerical results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. 相似文献
7.
P. G. Kazantzis 《Astrophysics and Space Science》1978,59(2):355-371
We consider the basic families of plane-symmetric simply-periodic orbits in the Sun-Jupiter case of the plane restricted three-body problem and we study their horizontal and vertical stabilities. We give the critical orbits of these families, corresponding to the vertical stability parameter = 1 and in future communications we shall give the three-dimensional families which emanate from these plane bifurcations. 相似文献
8.
Kathleen Connor Howell 《Celestial Mechanics and Dynamical Astronomy》1984,32(1):53-71
A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio , from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L1, the libration point between the two primaries, are there no stable orbits for certain values of . In that case the stable range decreases with increasing , until it disappears at =0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing . 相似文献
9.
The development and application of a predictor-corrector method for the computation of families of periodic motions as well as of singular periodic solutions from which branchings or change in the stability character occur, based on the use of second order variations is presented. Numerical results obtained by means of this method are also given. It is found that this algorithm consumes somewhat less computer time in determining orbits-members of a family of periodic orbits, while it represents a unique tool for the determination of branchings of various orders, as well as of the precise members of each family at which the orbits change from unstable to stable and viceversa. 相似文献
10.
P. G. Kazantzis 《Astrophysics and Space Science》1979,65(2):493-513
New families of three-dimensional double-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits (
v
= –1,c
v
),c
v=0) of the basic plane familiesi,g
1,g
2,h,a,m andl. Further the numerical procedure employed in the determination of these families has been described and interesting results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. 相似文献
11.
FranÇois Puel 《Celestial Mechanics and Dynamical Astronomy》1995,63(1):41-57
Using a generalization of Joukovsky's formula, we determine three-dimensional families of curves that are orbits only in separable potentials and we note the importance of iso-energetic families of orbits. We also obtain more general families that are orbits of partially separable systems and we examine from this point of view the classical curvilinear coordinate systems. 相似文献
12.
13.
Three-dimensional periodic motion of three finite masses around collinear equilibrium configurations
V. V. Markellos 《Celestial Mechanics and Dynamical Astronomy》1981,25(4):319-344
Three-dimensional periodic motions of three bodies are shown to exist in the infinitesimal neighbourhood of their collinear equilibrium configurations. These configurations and some characteristic quantities of the emanating three-dimensional periodic orbits are given for many values of the two mass parameters, =m
2/(m
1+m
2) andm
3, of the general three-body problem, under the assumption that the straight line containing the bodies at equilibrium rotates with unit angular velocity. The analysis of the small periodic orbits near the equilibrium configurations is carried out to second-order terms in the small quantities describing the deviation from plane motion but the analytical solution obtained for the horizontal components of the state vector is valid to third-order terms in those quantities. The families of three-dimensional periodic orbits emanating from two of the collinear equilibrium configurations are continued numerically to large orbits. These families are found to terminate at large vertical-critical orbits of the familym of retrograde periodic orbits ofm
3 around the primariesm
1 andm
2. The series of these termination orbits, formed when the value ofm
3 varies, are also given. The three-dimensional orbits are computed form
3=0.1. 相似文献
14.
The effect of small perturbations and in the coriolis and the centrifugal forces respectively on the stability of the triangular points in the restricted problem of three bodies with variable mass has been studied. It is found that the range of stability of triangular points increases or decreases depending upon whether the perturbation point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line J8–J9=0 where J8 and J9 depend upon , the constant due to the variation in mass governed by Jeans' law. 相似文献
15.
G. Contopoulos 《Celestial Mechanics and Dynamical Astronomy》1986,38(1):1-22
We study the bifurcations of families of double and quadruple period orbits in a simple Hamiltonian system of three degrees of freedom. The bifurcations are either simple or double, depending on whether a stability curve crosses or is tangent to the axis b=–2. We have also generation of a new family whenever a given family has a maximum or minimum or .The double period families bifurcate from simple families of periodic orbits. We construct existence diagrams to show where any given family exists in the control space (, ) and where it is stable (S), simply unstable (U), doubly unstable (DU), or complex unstable (), We construct also stability diagrams that give the stability parameters b1 and b2 as functions of (for constant ), or of (for constant ).The quadruple period orbits are generated either from double period orbits, or directly from simple period orbits (at double bifurcations). We derive several rules about the various types of bifurcations. The most important phenomenon is the collision of bifurcations. At any such collision of bifurcations the interconnections between the various families change and the general character of the dynamical system changes. 相似文献
16.
G. Contopoulos 《Celestial Mechanics and Dynamical Astronomy》1981,24(4):355-366
We study the resonance 12 = 41 and some near-resonance cases. The main peculiarity of this resonance is that for 12 < 4 the characteristic of the central periodic orbits is broken into two and each part is joined with a resonant characteristic. This behaviour is described theoretically by means of the third integral. It seems that there are infinite families of simple periodic orbits near the escape region. Finally, a comparison is made with the cases near the 12 = 21 resonance. 相似文献
17.
Jaume Llibre 《Celestial Mechanics and Dynamical Astronomy》1982,28(1-2):83-105
We study some aspects of the restricted three-body problem when the mass parameter is sufficiently small. First, we describe the global flow of the two-body rotating problem, =0, and we use it for the analysis of the collision and parabolic orbits when 0. Also we show that for any fixed value of the Jacobian constant and for any >0, there exists a 0>0 such that if the mass parameter [0,0], then the set of bounded orbits which are not contained in the closure of the set of symmetric periodic orbits has Lebesgue measure less than .Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics. 相似文献
18.
, . : , . , . . ( ) . . . HZ Her=Her X1, . . , . , ., hv 15–30 . , . Sco X1 . 相似文献
19.
An essential part in the mechanics under study is taking into consideration the effect of motions of the Universe objects upon that of an individual one surrounded by them including those infinitely far from it. Only macro-objects of the Universe are meant here.
Zusammenfassung Ein wesentlicher Bestandteil der Mechanik unter unserer Betrachtung ist die Berechnung des Einflusses auf die Bewegung eines individuellen Objektes von Bewegungen der Universum Objekte die es umringen einschließlich jene Objekte, die unendlich entfernt sind. Nur Makroobjekte des Weltalles sind in der Absicht dabei.
, . .相似文献
20.
, 1-, 2- 3- . , . 相似文献