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We study two and three-dimensional resonant periodic orbits, usingthe model of the restricted three-body problem with the Sun andNeptune as primaries. The position and the stability character ofthe periodic orbits determine the structure of the phase space andthis will provide useful information on the stability and longterm evolution of trans-Neptunian objects. The circular planarmodel is used as the starting point. Families of periodic orbitsare computed at the exterior resonances 1/2, 2/3 and 3/4 withNeptune and these are used as a guide to select the energy levelsfor the computation of the Poincaré maps, so that all basicresonances are included in the study. Using the circular planarmodel as the basic model, we extend our study to more realisticmodels by considering an elliptic orbit of Neptune and introducingthe inclination of the orbit. Families of symmetric periodicorbits of the planar elliptic restricted three-body problem andthe three-dimensional problem are found. All these orbitsbifurcate from the families of periodic orbits of the planarcircular problem. The stability of all orbits is studied. Althoughthe resonant structure in the circular problem is similar for allresonances, the situation changes if the eccentricity of Neptuneor the inclination of the orbit is taken into account. All theseresults are combined to explain why in some resonances there aremany bodies and other resonances are empty. 相似文献
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In the framework of the planar restricted three-body problem we study a considerable number of resonances associated to the basic dynamical features of Kuiper belt and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic orbits and their stability. Stable periodic orbits are surrounded by regular librations in phase space and in such domains the capture of trans-Neptunian object is possible. All the periodic orbits found are symmetric and there is an indication of the existence of asymmetric ones only in a few cases. In the present work first, second and third order resonances are under consideration. In the planar circular case we found that most of the periodic orbits are stable. The families of periodic orbits are temporarily interrupted by collisions but they continue up to relatively large values of the Jacobi constant and highly eccentric regular motion exists for all cases. In the elliptic problem and for a particular eccentricity value of the primary bodies, the periodic orbits are isolated. The corresponding families, where they belong to, bifurcate from specific periodic orbits of the circular problem and seem to continue up to the rectilinear problem. Both stable and unstable orbits are obtained for each case. In the elliptic problem, the unstable orbits found are associated with narrow chaotic domains in phase space. The evolution of the orbits, which are located in such chaotic domains, seems to be practically regular and bounded for long time intervals. 相似文献
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Comparative Study of the 2:3 and 3:4 Resonant Motion with Neptune: An Application of Symplectic Mappings and Low Frequency Analysis 总被引：2，自引：1，他引：1
The 2:3 and 3:4 exterior mean motion resonances with Neptune are studied by applying symplectic mapping models. The mappings
represent efficiently Poincaré maps for the 3D elliptic restricted three body problem in the neighbourhood of the particular
resonances. A large number of trajectories is studied showing the coexistence of regular and chaotic orbits. Generally, chaotic
motion depletes the small bodies of the effective resonant region in both the 2:3 and 3:4 resonances. Applying a low frequency
spectral analysis of trajectories, we determined the phase space regions that correspond to either regular or chaotic motion.
It is found that the phase space of the 3:4 resonant motion is more chaotic than the 2:3 one. 相似文献
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G. Voyatzis T. Kotoulas J. D. Hadjidemetriou 《Monthly notices of the Royal Astronomical Society》2009,395(4):2147-2156
The 2/1 resonant dynamics of a two-planet planar system is studied within the framework of the three-body problem by computing families of periodic orbits and their linear stability. The continuation of resonant periodic orbits from the restricted to the general problem is studied in a systematic way. Starting from the Keplerian unperturbed system, we obtain the resonant families of the circular restricted problem. Then, we find all the families of the resonant elliptic restricted three-body problem, which bifurcate from the circular model. All these families are continued to the general three-body problem, and in this way we can obtain a global picture of all the families of periodic orbits of a two-planet resonant system. The parametric continuation, within the framework of the general problem, takes place by varying the planetary mass ratio ρ. We obtain bifurcations which are caused either due to collisions of the families in the space of initial conditions or due to the vanishing of bifurcation points. Our study refers to the whole range of planetary mass ratio values [ρ∈ (0, ∞)] and, therefore we include the passage from external to internal resonances. Thus, we can obtain all possible stable configurations in a systematic way. As an application, we consider the dynamics of four known planetary systems at the 2/1 resonance and we examine if they are associated with a stable periodic orbit. 相似文献
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Astrophysics and Space Science - Fast radio bursts (FRBs) are extremely strong radio flares lasting several micro- to milliseconds and come from unidentified objects at cosmological distances, most... 相似文献
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A. Celletti T. Kotoulas G. Voyatzis J. Hadjidemetriou 《Monthly notices of the Royal Astronomical Society》2007,378(3):1153-1164
The dynamics of the Kuiper Belt region between 33 and 63 au is investigated just taking into account the gravitational influence of Neptune. Indeed the aim is to analyse the information which can be drawn from the actual exoplanetary systems, where typically physical and orbital data of just one or two planets are available. Under this perspective we start our investigation using the simplest three-body model (with Sun and Neptune as primaries), adding at a later stage the eccentricity of Neptune and the inclinations of the orbital planes to evaluate their effects on the Kuiper Belt dynamics. Afterwards we remove the assumption that the orbit of Neptune is Keplerian by adding the effect of Uranus through the Lagrange–Laplace solution or through a suitable resonant normal form. Finally, different values of the mass ratios of the primary to the host star are considered in order to perform a preliminary analysis of the behaviour of exoplanetary systems. In all cases, the stability is investigated by means of classical tools borrowed from dynamical system theory, like Poincaré mappings and Lyapunov exponents. 相似文献
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G. Voyatzis T. Kotoulas J.D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2005,91(1-2):191-202
We present families of periodic orbits and their stability for the exterior mean motion resonances 1:2, 1:3 and 1:4 with Neptune
in the framework of the planar circular restricted three-body problem. We found that in each resonance there exist two branches
of symmetric elliptic periodic orbits with stable and unstable segments. Asymmetric periodic orbits bifurcate from the corresponding
symmetric ones. Asymmetric periodic orbits are stable and the motion in their neighbourhood is a libration with respect to
the resonant angle variable. In all the families of asymmetric periodic orbits the eccentricity extends to high values. Poincaré
sections reveal the changes of the topology in phase space. 相似文献
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I.S. Travlos G. Economou V.E. Kotoulas P.J. Kanatas A.N. Kontogeorgos A.I. Karamanos 《Journal of Arid Environments》2009,73(1):22-25
Purple nutsedge (Cyperus rotundus L.) is one of the most serious weed problems of the arid environments. The distribution of its tubers in a naturally infested field in Greece indicated that the highest proportion is located in the upper 200 mm of the soil. Furthermore, the effects of temperature alternation on the rate and percentage of tuber sprouting were evaluated by means of laboratory studies. It was found that the total tuber sprouting and rate were significantly increased after a shift of daily temperature fluctuation from 0 to 12 °C. Sprouting rate and percentage were significantly and consistently higher for the tubers originating from the upper 5 cm of the soil, compared with the tubers obtained from the layer of 50–150 mm for all the temperature treatments. Additionally, solarization seems potentially effective on purple nutsedge tuber sprouting, as long as it resulted not only to a soil temperature shift, but also to a high diurnal temperature variation. Moreover, the uniform sprouting of about 95% of the tubers in the soil may allow a more complete control by mechanical, biological or chemical methods. 相似文献
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