Resonant Periodic Orbits of Trans-Neptunian Objects     

Kotoulas  Thomas A.  Hadjidemetriou  John D. 《Earth, Moon, and Planets》2002,91(2):63-93

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   

Theory of satellite ground-track crossovers     

M. C. Kim 《Journal of Geodesy》1997,71(12):749-767

The fundamental geometry of satellite ground tracks and their crossover problem are investigated. For idealized nominal ground tracks, the geometry is governed by a few constant parameters whose variations lead to qualitative changes in the crossover solutions. On the basis that the theory to locate crossovers has not been studied in sufficient detail, such changes are described in regard to the number of crossover solutions in conjunction with their bifurcations. Employing the spinor algebra as a tool for establishing the ground-track crossing condition, numerical methodologies to locate crossovers appearing in general dual-satellite ground-track configurations are also presented. The methodologies are applied to precisely determined orbital ephemerides of the GEOSAT, ERS-1, and TOPEX/POSEIDON altimeter satellites. Received: 19 November 1996 / Accepted: 12 May 1997  相似文献   

Dissipative systems: Implications for geomorphology     

R. J. Huggett 《地球表面变化过程与地形》1988,13(1):45-49

A recent revolution in the study of nonlinear dynamical systems in the physical sciences has shown the worth of regarding systems as dissipative. The nature of dissipative systems in equations, bifurcations, and fluctuations. Some speculations are then made concerning the implications of dissipative system theory for geomorphology. It is suggested that geomorphological systems containing bifurcations will have both deterministic (universal and necessary) and probabilistic (historical happenstance) elements; they will have more than one solution (configuration) and this fact calls into question notions of process domains leading to the development of characteristic forms; they will possess varying degrees of susceptibility to change induced by fluctuations; and they will respond differently to local, regional, and global fluctuations.  相似文献   

亮点周围的衍射模式          下载免费PDF全文

刘伟霞  栾文贵 《地球物理学报》1994,37(3):370-381

将衍射问题研究中的回波解析奇性归结为探讨含参量的振荡积分的渐近性态问题，并利用广义函数的算子理论，以十分简捷的方式给出了上述振荡积分的稳定位相公式，以及结合Ｔｈｏｍ理论逐一地算出非退化奇点、岐点和脐点周围的衍射模式．  相似文献   

冬季平流层波动模型的分岔特性          下载免费PDF全文

胡雄  张训械  黄信榆 《地球物理学报》1995,(4)

从描述波流相互作用的Ｈｏｌｔｏｎ－Ｄｕｎｋｅｒｔｏｎ简称Ｈ－Ｄ）模型出发，应用延拓方法求解常微分方程的分岔问题，研究冬季平流层波动模型的分岔特性．给出了大气行星波２与流相互作用的底部边界强迫波、底部边界平均纬向风场、风切变等参数的分岔特性，同时给出了波１与流相互作用的底部边界强迫波的分岔特性的结果．  相似文献   

Compaction localization in the Earth and the laboratory: state of the research and research directions   总被引：1，自引：1，他引：1  

David Holcomb  John W. Rudnicki  Kathleen A. Issen  Kurt Sternlof 《Acta Geotechnica》2007,2(1):1-15

Localized compaction in porous rocks is a recently recognized phenomenon that has been shown to reduce permeability dramatically. Consequently, the phenomenon is relevant to a variety of technologies involving fluid injection or withdrawal. This article summarizes current understanding of localized compaction and impediments to further progress. The article is based on discussions at a small workshop on localized compaction sponsored by the Office of Science, U. S. Department of Energy.  相似文献   

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field     

J. F. Palacián 《Celestial Mechanics and Dynamical Astronomy》2007,98(4):219-249

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.  相似文献   

非线性层结与对流运动的稳定性     

陈忠明 《成都信息工程学院学报》1991,(Z1)

本文讨论了温度层结为普遍化三次分布情况下对流运动的分岔和突变特征,得到了一些有意义的结果,加深了我们对非线性对流运动特征的一些认识。  相似文献   

静力平衡近似下大气中非线性对称运动的稳定性、分岔和突变     

彭晓林  罗德海 《成都信息工程学院学报》1991,(Z1)

本文在考虑基本气流具有非线性切变情况下,导出了对称运动所满足的非线性常微分方程,并用非线性系统的稳定、分岔、突变理论,严格地讨论了非线性对称运动的稳定性、分岔和突变问题,获得了一个推广的对称不稳定判据,找到了突变产生的条件。  相似文献   

The restricted two-body problem in constant curvature spaces     

Alexey V. Borisov  Ivan S. Mamaev 《Celestial Mechanics and Dynamical Astronomy》2006,96(1):1-17

We perform the bifurcation analysis of the Kepler problem on and . An analog of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of a Newtonian center moving along a geodesic on and (the restricted two-body problem). For the case of a small curvature, the pericenter shift is computed using the perturbation theory. We also present the results of numerical analysis based on an analogy with the motion of a rigid body.  相似文献