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141.
D. J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》1998,70(2):75-98
Starting from the four-body problem a generalization of both the restricted three-body problem and the Hill three-body problem
is derived. The model is time periodic and contains two parameters: the mass ratio ν of the restricted three-body problem
and the period parameter m of the Hill Variation orbit. In the proper coordinate frames the restricted three-body problem
is recovered as m → 0 and the classical Hill three-body problem is recovered as ν → 0. This model also predicts motions described
by earlier researchers using specific models of the Earth–Moon–Sun system. An application of the current model to the motion
of a spacecraft in the Sun perturbed Earth–Moon system is made using Hill's Variation orbit for the motion of the Earth–Moon
system. The model is general enough to apply to the motion of an infinitesimal mass under the influence of any two primaries
which orbit a larger mass.
Using the model, numerical investigations of the structure of motions around the geometric position of the triangular Lagrange
points are performed. Values of the parameter ν range in the neighborhood of the Earth–Moon value as the parameter m increases
from 0 to 0.195 at which point the Hill Variation orbit becomes unstable. Two families of planar periodic orbits are studied
in detail as the parameters m and ν vary. These families contain stable and unstable members in the plane and all have the
out-of-plane stability. The stable and unstable manifolds of the unstable periodic orbits are computed and found to be trapped
in a geometric area of phase space over long periods of time for ranges of the parameter values including the Earth–Moon–Sun
system.
This model is derived from the general four-body problem by rigorous application of the Hill and restricted approximations.
The validity of the Hill approximation is discussed in light of the actual geometry of the Earth–Moon–Sun system.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
142.
A method for determining the main families of isolated periodic orbits and their characteristic exponents in planar potentials
which are separated by a point transformation is proposed. Since these orbits are continued analytically with the same stability,
these results are persistent under small perturbations. The method is applied to the two fixed centers problem, the Paul trap
and the dipole expansion of an electrostatic potential.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
143.
Mass-weighted symplectic forms provide a unified framework for the treatment of both finite and vanishingly small masses in
the N-body problem. These forms are introduced, compared to previous approaches, and their properties are discussed. Applications
to symplectic mappings, the definition of action-angle variables for the Kepler problem, and Hamiltonian perturbation theory
are outlined
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
144.
We study the motion of an infinitesimal mass point under the gravitational action of three mass points of masses μ, 1–2μ and
μ moving under Newton's gravitational law in circular periodic orbits around their center of masses. The three point masses
form at any time a collinear central configuration. The body of mass 1–2μ is located at the center of mass. The paper has
two main goals. First, to prove the existence of four transversal ejection–collision orbits, and second to show the existence
of an uncountable number of invariant punctured tori. Both results are for a given large value of the Jacobi constant and
for an arbitrary value of the mass parameter 0<μ≤1/2.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
145.
An integrated wavelet concept of physical geodesy 总被引:4,自引:1,他引:3
For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial
gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection
between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept
of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can
be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical
geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an
integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing
the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential
outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of
band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding
to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique
derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking
and gradiometry.
Received: 28 February 1997 / Accepted: 17 November 1997 相似文献
146.
GUO Junyi Associate Professor Laboratory for Modern Geodynamics WTUSM Wuhan China 《地球空间信息科学学报》1998,(1)
In this paper,a variational method is presented for solving theclassical gravimetric,satellite gravimetric and satellite altimetric mixed typeboudary value problem to obtain the potential coefficients.According to thisprinciple,classical gravimetric data(height measured by geometric levelling orheight triangulation),satellite gravimetric data(height measured by satellitegeodesy technique)and satellite altimetric data can be used jointly to calculate thepotential coefficients. 相似文献
147.
提出内蕴大地边值问题,使得有可能利用重力场边界观测研究地球重力场的内蕴结构。文中构造了椭球问题的迭代逼近求解程式,并给出了具体解式。 相似文献
148.
扩散波的时空反演与洪水实时预报技术 总被引:2,自引:1,他引:1
以扩散波方程描述天然河道中的洪水波运动规律。将数学物理反问题理论和离散反演算法与河道流量演算相结合提出了扩散波实时预报的方法。该法的特点是在求解流量场Q(x,t)的同时反演计算扩散波波速C(x,t)和扩散系数D(x,t),根据不断监测的新信息系列,直接利用原偏微分方程进行参数的实时校正和预报过程实时修正。 相似文献
149.
150.
Izuru Takewaki Tsuneyoshi Nakamura Kitae Hirayama 《Soil Dynamics and Earthquake Engineering》1998,17(3):153-163
A two-step stiffness design procedure is developed for a moment-resisting planar frame supported by a prescribed two-dimensional finite-element ground-pile system. In the first step, a hybrid inverse eigenmode problem is formulated and its solution is derived in an analytical form. A difficulty resulting from the existence of multiple interface nodes is overcome by incorporating a deformation constraint into a set of linear equations for finding the lowest-mode displacements at the interface nodes and in the ground. In the second step, the fundamental natural frequency of the combined system and the lowest mode-strain ratios in the frame specified in the first step are regarded as the parameters for adjusting the mean peak seismic member-end strains to their specified values. If the fundamental natural frequency of the frame with a fixed-base happens to be close to that of the ground, a difficulty arises in the two-step stiffness design procedure because of an irregular response amplification and of the non-predominance of the lowest-mode components. A new practical design procedure of rapid convergence is proposed such that an initial design is found for a stiff ground and that a sequence of stiffness designs is generated with respect to a ground stiffness parameter without any differential coefficient of series expansion. The accuracy of the model utilized in this paper and the validity of the present stiffness design procedure are verified through time-history response analysis. 相似文献