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921.
Roberto Armellin Francesco Topputo 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):289-309
A sixth-order accurate scheme is presented for the solution of ODE systems supplemented by two-point boundary conditions. The proposed integration scheme is a linear multi-point method of sixth-order accuracy successfully used in fluid dynamics and implemented for the first time in astrodynamics applications. A discretization molecule made up of just four grid points attains a O(h
6) accuracy which is beyond the first Dahlquist’s stability barrier. Astrodynamics applications concern the computation of libration point halo orbits, in the restricted three- and four-body models, and the design of an optimal control strategy for a low thrust libration point mission. 相似文献
922.
Starting from the identification and classification of a family of fast periodic transfer orbits in the Earth–Moon planar
circular Restricted Three Body Problem (RTBP), and using analytic continuation techniques, we find two unstable periodic orbits
in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). The orbits found perform periodic Earth–Moon transfers with a period
of approximately 29.5 days. 相似文献
923.
We study the chaotic motions in the field of two fixed black holes M1, M2 by calculating (a) the asymptotic curves from the main unstable periodic orbits, (b) the asymptotic orbits, with particular emphasis οn the homoclinic and heteroclinic orbits, and (c) the basins of attraction of the two black holes. The orbits falling on M1and M2form fractal sets. The asymptotic curves consist of many arcs, separated by gaps. Every gap contains orbits falling on a black hole. The sizes of various arcs decrease as the mass ofM1 increases. The basins of attraction of the black holes M1, M2consist of large compact regions and of thin filaments. The relative area of the basin M2 tends to 100 as M1 → 0, and it decreases as M1 increases. The total area of the basins is found analytically, while the relative area of the basin M2 is given by an empirical formula. Further empirical formulae give the exponential decrease of the number of asymptotic orbits that have not yet reached a black hole after n iterations. 相似文献
924.
Sebastián Ferrer Juan Félix San-Juan Alberto Abad 《Celestial Mechanics and Dynamical Astronomy》2007,99(1):69-83
In the analytical approach to the main problem in satellite theory, the consideration of the physical parameters imposes a
lower bound for normalized Hamiltonian. We show that there is no elliptic frozen orbits, at critical inclination, when we
consider small values of H, the third component of the angular momentum. The argument used suggests that it might be applied also to more realistic
zonal and tesseral models. Moreover, for almost polar orbits, when H may be taken as another small parameter, a different approach that will simplify the ephemerides generators is proposed. 相似文献
925.
The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body
problem. This family is unusual in that it is a simplex stacked central configuration, i.e the bodies are arranged as concentric three and two dimensional simplexes.
相似文献
926.
C. Marchal 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):123-134
The famous Laplace problem is the three-body, secular, planetary problem. Its plane version has the great theoretical advantage of being integrable (Ferraz-Mello, private correspondence, 2001) and Ferraz-Mello et al. (Chaotic World: from order to Disorder in Gravitational N-Body Systems, Kluwer Academic Publisher, 2004)). Nevertheless it remains a very complex problem with many singularities and many possibilities of collisions. Large eccentricities lead generally to large perturbations especially if the two planets have the same direction of revolution about their star. 相似文献
927.
T.J. Kalvouridis 《Planetary and Space Science》2004,52(10):909-914
Zero-velocity curves are a useful tool in the investigation of various aspects of a dynamical system. These curves that distinguish the regions where the motion of a particle is permissible from the regions where this motion is not permitted, present some basic properties. In this paper, we prove that in symmetric ring-type systems where a small particle moves under the resultant gravitational field of N coplanar big bodies, of which ν=N−1 are arranged at equal distances among them on the periphery of a circle, a new property concerning these curves, exists. All the zero-velocity curves drawn in the space of the initial conditions (x0,C) and concerning configurations with the same number of peripheral primaries but various mass parameters, pass through two different focal points, the position of which does not depend on the value of the mass parameter. 相似文献
928.
Seppo Mikkola 《Celestial Mechanics and Dynamical Astronomy》1997,67(2):145-165
The use of the extended phase space and time transformations for constructing efficient symplectic algorithms for the investigation
of long term behavior of hierarchical few-body systems is discussed. Numerical experiments suggest that the time-transformed
generalized leap-frog, combined with symplectic correctors, is one of the most efficient methods for such studies. Applications
extend from perturbed two-body motion to hierarchical many-body systems with large eccentricities.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
929.
Consecutive collision orbits in the limiting case µ = 0 of the elliptic restricted three-body problem are investigated. in particular those in which the infinitesimal mass collides twice with the smaller (massless) primary. A timing condition is presented that allows the extension of previous results to the case of arbitrary relative orientation of the orbits of the infinitesimal mass and the smaller primary. The timing condition is expressed in two general forms - in terms of orbit parameters and eccentric (or hyperbolic) anomalies at the times of collision - for the specific cases of elliptic. parabolic or hyperbolic orbits of the infinitesimal mass. Some families of solutions are presented. 相似文献
930.
Mordehai Milgrom 《New Astronomy Reviews》2002,46(12):217
I discuss open theoretical questions pertaining to the modified dynamics (MOND)—a proposed alternative to dark matter, which posits a breakdown of Newtonian dynamics in the limit of small accelerations. In particular, I point the reasons for thinking that MOND is an effective theory—perhaps, despite appearance, not even in conflict with GR. I then contrast the two interpretations of MOND as modified gravity and as modified inertia. I describe two mechanical models that are described by potential theories similar to (non-relativistic) MOND: a potential-flow model, and a membrane model. These might shed some light on a possible origin of MOND. The possible involvement of vacuum effects is also speculated on. 相似文献