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171.
172.
A Counterexample to a Generalized Saari's Conjecture with a Continuum of Central Configurations 总被引:1,自引:1,他引:0
Manuele Santoprete 《Celestial Mechanics and Dynamical Astronomy》2004,89(4):357-364
In this paper we show that in the n-body problem with harmonic potential one can find a continuum of central configurations for n= 3. Moreover we show a counterexample to an interpretation of Jerry Marsden Generalized Saari's conjecture. This will help
to refine our understanding and formulation of the Generalized Saari's conjecture, and in turn it might provide insight in
how to solve the classical Saari's conjecture for n≥ 4.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
173.
L. G. Luk’yanov 《Astronomy Letters》2005,31(8):563-568
We consider the conservative two-body problem with a constant total mass, but with variable individual masses. The problem is shown to be completely integrable for any mass variation law. The Keplerian motion known for the classical two-body problem with constant masses remains valid for the relative motion of the bodies. The absolute motions of the bodies depend on the center-of-mass motion. Hitherto unknown quadratures that depend on the mass variation law were derived for the integrals of motion of the center of mass. We consider some of the laws that are of interest in studying the motion of close binary stars with mass transfer. 相似文献
174.
D. Viswanath 《Celestial Mechanics and Dynamical Astronomy》2006,94(2):213-235
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses
1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle
in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions.
We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study
of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem
are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations
to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances.
We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3,
and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist
for μ small enough in the unaveraged restricted three-body problem. 相似文献
175.
Mutual Potential of Homogeneous Polyhedra 总被引:2,自引:0,他引:2
Robert A. Werner Daniel J. Scheeres 《Celestial Mechanics and Dynamical Astronomy》2005,91(3-4):337-349
The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested
volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However,
complexity increases as O(6
n
), where n is the term degree. An alternate formulation due to Liebenthal is also presented. 相似文献
176.
C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》2004,88(1):51-68
In this communication we present an analytical model for the restricted three-body problem, in the case where the perturber is in a parabolic orbit with respect to the central mass. The equations of motion are derived explicitly using the so-called Global Expansion of the disturbing function, and are valid for any eccentricity of the massless body, as well as in the case where both secondary masses have crossing orbits. Integrating the equations of motion over the complete passage of the perturber through the system, we are then able to construct a first-order algebraic mapping for the change in semimajor axis, eccentricity and inclination of the perturbed body.Comparisons with numerical solutions of the exact equations show that the map yields precise results, as long as the minimum distance between both bodies is not too small. Finally, we discuss several possible applications of this model, including the evolution of asteroidal satellites due to background bodies, and simulations of passing stars on extra-solar planets. 相似文献
177.
文章指出加强地质科技档案鉴定销毁工作的紧迫性 ,对影响该项工作开展的因素与解决对策进行了论述。 相似文献
178.
A full characterization of a nonintegrable dynamical system requires an investigation into the chaotic properties of that system. One such system, the restricted problem of three bodies, has been studied for over two centuries, yet few studies have examined the chaotic nature of some ot its trajectories. This paper examines and classifies the onset of chaotic motion in the restricted three-body problem through the use of Poincaré surfaces of section, Liapunov characteristic numbers, power spectral density analysis and a newly developed technique called numerical irreversibility. The chaotic motion is found to be intermittent and becomes first evident when the Jacobian constant is slightly higher thanC
2. 相似文献
179.
Maria Dina Vivarelli 《Celestial Mechanics and Dynamical Astronomy》1994,60(3):291-305
This paper is an attempt to bring unity in the study of the classical Kepler problem by combining, through simple vectorial and quaternionic techniques, its two peculiar aspects: the determination of the constants of the motion and the regularization at the origin.Research supported by the Consiglio Nazionale delle Ricerche of Italy (C.N.R.-G.N.F.M.). 相似文献
180.
C. M. Giordano A. R. Plastino A. Plastino 《Celestial Mechanics and Dynamical Astronomy》1996,66(2):229-242
Robe's restricted three-body problem is investigated with regards to the effects of a linear drag force. In particular. the stability of the model's equilibrium points is studied in this respect. Two scenarios are envisaged: the one originally discussed by Robe himself and the one suggested by him and recently analyzed by the present authors, that assumes for the fluid body the structure of a Roche's ellipsoid. 相似文献