Periodic orbits emanating from a resonant equilibrium     

Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1970,1(3-4):437-466

For a conservative Hamiltonian system with two degrees of freedom, in the case where the two frequencies at an equilibrium of the elliptic type are commensurable or close to being so, completely canonical transformations can be formally constructed in explicit terms under the form of Lie transforms to the effect that it renders one angle coordinate ignorable and gives to the transformed Hamiltonian the form of what Garfinkel calls an ideal problem of resonance. For the problem so reduced, the unnormalized residual being omitted, natural families of periodic orbits are analyzed, their emergence from the equilibrium is discussed as well as their characteristic exponents. Special attention is given to the evolution of the system of natural families under a continuous transition through the resonance band.  相似文献   

Seismic scattering and shallow structure of the moon in oceanus procellarum   总被引：1，自引：0，他引：1  

Anton M. Dainty  M. Nafi Toksöz  Kenneth R. Anderson  P. Jacques Pines  Y. Nakamura  G. Latham 《Earth, Moon, and Planets》1974,9(1-2):11-29

Long, reverberating trains of seismic waves produced by impacts and moonquakes may be interpreted in terms of scattering in a surface layer overlying a non-scattering elastic medium. Model seismic experiments are used to qualitatively demonstrate the correctness of the interpretation. Three types of seismograms are found, near impact, far impact and moonquake. Only near impact and moonquake seismograms contain independent information. Details are given in the paper of the modelling of the scattering processes by the theory of diffusion.Interpretation of moonquake and artificial impact seismograms in two frequency bands from the Apollo 12 site indicates that the scattering layer is 25 km thick, with a Q of 5000. The mean distance between scatterers is approximately 5 km at 25 km depth and approximately 2 km at 14 km depth; the density of scatterers appears to be high near the surface, decreasing with depth. This may indicate that the scatterers are associated with cratering, or are cracks that anneal with depth. Most of the scattered energy is in the form of scattered surface waves.Communication presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.  相似文献   

Central forces depending on the distance only. Case where all the bounded orbits are periodic     

Jacques Roels  Christine Aerts 《Celestial Mechanics and Dynamical Astronomy》1988,44(1-2):77-85

It is shown in this paper that the only potentials corresponding to central force for which all the bounded orbits are periodic are the potential of the harmonic oscillator and of the two body problem. A discussion is given in the case where a circular orbit exists and when the orbits near the circular orbit are periodic.We calculate in these cases the angle between pericentre and apocentre.Celestial Mechanics  相似文献   

Elasto-Gravitational Deformation, Relative Gravity Changes and Earth dynamics     

Jacques Hinderer  Hilaire Legros 《Geophysical Journal International》1989,97(3):481-495

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Preface     

Jean Chapront  Jacques Henrard  Dieter Schmidt 《Celestial Mechanics and Dynamical Astronomy》1982,26(1):2-3

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The dynamics of the upper ocean: 2nd edn. O.M. Phillips. Cambridge University Press,Cambridge, 1980, viii + 336 pp., 67 illus., U.K. £ 7.95 (paperback).     

Jacques C.J. Nihoul 《Dynamics of Atmospheres and Oceans》1981,5(4):308

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A new solution to the Main Problem of Lunar Theory     

Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1979,19(4):337-355

A new solution for the Main Problem on Lunar Theory is given. This solution maintains the advantages of an analytical solution and should be more accurate than previous analytical or numerical solutions. It contains the effects of the mass ratios which are often neglected in the definition of the Main Problem.  相似文献   

On a perturbation theory using Lie transforms     

Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1970,3(1):107-120

Kamel has recently extended to non-Hamiltonian equations a perturbation theory using Lie transforms. We show here how Kamel's extension can be approached from an intrinsic viewpoint, which reformulation leads to a simpler algorithm. Then we complete Kamel's contribution by establishing the rules for inverting the transformation generated by the perturbation theory, and for composing two such transformations.  相似文献   

The line response function of stellar atmospheres and the effective depth of line formation     

Jacques M. Beckers  Robert W. Milkey 《Solar physics》1975,43(2):289-292

The response function defines the response of line profiles to a depth variation of such atmospheric parameters as velocity, magnetic field and turbulence. The properties of this function are derived and compared with the so-called contribution function.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.  相似文献   

Normalisation des systèmes linéaires canoniques et application au problème restreint des trois corps     

Jacques Roels  Georges Louterman 《Celestial Mechanics and Dynamical Astronomy》1970,3(1):129-140

An algorithm is given for normalizing conservative linear Hamiltonian systems. This one generalizes Siegel's method to the cases where the eigenvalues are multiple. We obtain by a canonical transformation a normal form of two blocks, one of which is the upper Jordan form, and the other, the lower Jordan form. We select real solutions from the solutions of these equations, and we apply the result to the restricted three body problem in the vicinity of the triangular points for Routh's critical mass ratio.

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_n est la matrice unité d'ordren,O _n est la matrice nulle d'ordren.  相似文献