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1.
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
2.
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
3.
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
4.
5.
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
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
6.
7.
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
8.
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
9.
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
10.