排序方式： 共有42条查询结果，搜索用时 24 毫秒
11.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1975,12(3):255-276
A method is developed to study the stability of periodic motions of the three-body problem in a rotating frame of reference, based on the notion of surface of section. The method is linear and involves the computation of a 4×4 variational matrix by integrating numerically the differential equations for time intervals of the order of a period. Several properties of this matrix are proved and also it is shown that for a symmetric periodic motion it can be computed by integrating for half the period only.This linear stability analysis is used to study the stability of a family of periodic motions of three bodies with equal masses, in a rotating frame of reference. This family represents motion such that two bodies revolve around each other and the third body revolves around this binary system in the same direction to a distance which varies along the members of the family. It was found that a large part of the family, corresponding to the case where the distance of the third body from the binary system is larger than the dimensions of the binary system, represents stable motion. The nonlinear effects to the linear stability analysis are studied by computing the intersections of several perturbed orbits with the surface of sectiony
3=0. In some cases more than 1000 intersections are computed. These numerical results indicate that linear stability implies stability to all orders, and this is true for quite large perturbations. 相似文献
12.
George Voyatzis John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):263-294
Families of asymmetric periodic orbits at the 2/1 resonance are computed for different mass ratios. The existence of the asymmetric
families depends on the ratio of the planetary (or satellite) masses. As models we used the Io-Europa system of the satellites
of Jupiter for the case m1>m2, the system HD82943 for the new masses, for the case m1=m2 and the same system HD82943 for the values of the masses m1<m2 given in previous work. In the case m1≥ m2 there is a family of asymmetric orbits that bifurcates from a family of symmetric periodic orbits, but there exist also an
asymmetric family that is independent of the symmetric families. In the case m1<m2 all the asymmetric families are independent from the symmetric families. In many cases the asymmetry, as measured by
and by the mean anomaly M of the outer planet when the inner planet is at perihelion, is very large. The stability of these asymmetric families has
been studied and it is found that there exist large regions in phase space where we have stable asymmetric librations. It
is also shown that the asymmetry is a stabilizing factor. A shift from asymmetry to symmetry, other elements being the same,
may destabilize the system. 相似文献
13.
We present a symplectic mapping model to study the evolution of a small body at the 3/4 exterior resonance with Neptune, for planar and for three dimensional motion. The mapping is based on the averaged Hamiltonian close to this resonance and is constructed in such a way that the topology of its phase space is similar to that of the Poincaré map of the elliptic restricted three-body problem. Using this model we study the evolution of a small object near the 3/4 resonance. Both chaotic and regular motions are found, and it is shown that the initial phase of the object plays an important role on the appearance of chaos. In the planar case, objects that are phase-protected from close encounters with Neptune have regular orbits even at eccentricities up to 0.44. On the other hand objects that are not phase protected show chaotic behaviour even at low eccentricities. The introduction of the inclination to our model affects the stable areas around the 3/4 mean motion resonance, which now become thinner and thinner and finally at is=10° the whole resonant region becomes chaotic. This may justify the absence of a large population of objects at this resonance. 相似文献
14.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):379-393
Recent results on periodic orbits are presented. Planetary systems can be studied by the model of the general 3-body problem and also some satellite systems and asteroid orbits can be studied by the model of the restricted 3-body problem. Triple stellar systems and planetary systems with two Suns are close to periodic systems. Finally, the motion of stars in various types of galaxies can be studied by finding families of periodic orbits in several galactic models. 相似文献
15.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):65-76
We present a 3-D symplectic mapping model that is valid at the 2:1 mean motion resonance in the asteroid motion, in the Sun-Jupiter-asteroid
model. This model is used to study the dynamics inside this resonance and several features of the system have been made clear.
The introduction of the third dimension, through the inclination of the asteroid orbit, plays an important role in the evolution
of the asteroid and the appearance of chaotic motion. Also, the existence of the secondary resonances is clearly shown and
their role in the appearance of chaotic motion and the slow diffusion of the elements of the orbit is demonstrated.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
Dionyssia Psychoyos John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):135-156
A complete study is made of the resonant motion of two planets revolving around a star, in the model of the general planar three body problem. The resonant motion corresponds to periodic motion of the two planets, in a rotating frame, and the position and stability properties of the periodic orbits determine the topology of the phase space and consequently play an important role in the evolution of the system. Several families of symmetric periodic orbits are computed numerically, for the 2/1 resonance, and for the masses of some observed extrasolar planetary systems. In this way we obtain a global view of all the possible stable configurations of a system of two planets. These define the regions of the phase space where a resonant extrasolar system could be trapped, if it had followed in the past a migration process.The factors that affect the stability of a resonant system are studied. For the same resonance and the same planetary masses, a large value of the eccentricities may stabilize the system, even in the case where the two planetary orbits intersect. The phase of the two planets (position at perihelion or aphelion when the star and the two planets are aligned) plays an important role, and the change of the phase, other things being the same, may destabilize the system. Also, the ratio of the planetary masses, for the same total mass of the two planets, plays an important role and the system, at some resonances and some phases, is destabilized when this ratio changes.The above results are applied to the observed extrasolar planetary systems HD 82943, Gliese 876 and also to some preliminary results of HD 160691. It is shown that the observed configurations are close to stable periodic motion. 相似文献
17.
John D. Hadjidemetriou 《Astrophysics and Space Science》1968,1(3):336-346
The effects of a series of isotropic ejections of small amounts of mass from either component of a binary system are studied. The evolution is completely different than in the case where all the mass is lost at once. When the ejections are randomly distributed in time, the final eccentricity may become larger or smaller than the initial one; the differences, however, are in most cases small. When the frequency of the explosions is higher near periastron, the final eccentricity is in most cases larger than the original value. In almost no case the system is disrupted. 相似文献
18.
John D. Hadjidemetriou Th. Christides 《Celestial Mechanics and Dynamical Astronomy》1975,12(2):175-187
A periodic orbit of the restricted circular three-body problem, selected arbitrarily, is used to generate a family of periodic motions in the general three-body problem in a rotating frame of reference, by varying the massm 3 of the third body. This family is continued numerically up to a maximum value of the mass of the originally small body, which corresponds to a mass ratiom 1:m 2:m 3?5:5:3. From that point on the family continues for decreasing massesm 3 until this mass becomes again equal to zero. It turns out that this final orbit of the family is a periodic orbit of the elliptic restricted three body problem. These results indicate clearly that families of periodic motions of the three-body problem exist for fixed values of the three masses, since this continuation can be applied to all members of a family of periodic orbits of the restricted three-body problem. It is also indicated that the periodic orbits of the circular restricted problem can be linked with the periodic orbits of the elliptic three-body problem through periodic orbits of the general three-body problem. 相似文献
19.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1982,27(3):305-322
The factors which affect the linear stability of a periodic planetary orbit in the plane are studied. It is proved that planetary systems with two planets describing nearly circular orbits in the same direction are linearly stable and no perturbation exists which destroys the stability, unless a resonance of the form 1/3, 3/5, 5/7, ... among the orbits of the planets occurs. This latter resonant case is always unstable. Retrograde motion is always linearly stable. Planetary systems with three or more planets in nearly circular orbits in the same direction are proved to be unstable, in the sense that a Hamiltonian perturbation always exists which destroys the stability. The generation of instability in the case of three or more planets is not only due to the existence of resonances, as in the case of two planets, but also to the nonexistence of integrals of motion, apart from the energy and angular momentum integrals. It is also proved that planetary systems with nearly elliptic orbits of the planets are unstable. 相似文献
20.
We have shown, in previous publications, that stable chaos is associated with medium/high-order mean motion resonances with Jupiter, for which there exist no resonant periodic orbits in the framework of the elliptic restricted three-body problem. This topological “defect” results in the absence of the most efficient mechanism of eccentricity transport (i.e., large-amplitude modulation on a short time scale) in three-body models. Thus, chaotic diffusion of the orbital elements can be quite slow, while there can also exist a nonnegligible set of chaotic orbits which are semiconfined (stable chaos) by “quasi-barriers” in the phase space. In the present paper we extend our study to all mean motion resonances of order q≤9 in the inner main belt (1.9-3.3 AU) and q≤7 in the outer belt (3.3-3.9 AU). We find that, out of the 34 resonances studied, only 8 possess resonant periodic orbits that are continued from the circular to the elliptic three-body problem (regular families), namely, the 2/1, 3/1, 4/1, and 5/2 in the inner belt and the 7/4, 5/3, 11/7, and 3/2 in the outer belt. Numerical results indicate that the 7/3 resonance also carries periodic orbits but, unlike the aforementioned resonances, 7/3-periodic orbits belong to an irregular family. Note that the five inner-belt resonances that carry periodic orbits correspond to the location of the main Kirkwood gaps, while the three outer-belt resonances correspond to gaps in the distribution of outer-belt asteroids noted by Holman and Murray (1996, Astron. J.112, 1278-1293), except for the 3/2 case where the Hildas reside. Fast, intermittent eccentricity increase is found in resonances possessing periodic orbits. In the remaining resonances the time-averaged elements of chaotic orbits are, in general, quite stable, at least for times t∼250 Myr. This slow diffusion picture does not change qualitatively, even if more perturbing planets are included in the model. 相似文献