A note concerning the 2:1 and the 3:2 resonances in the asteroid belt     

Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1996,64(1-2):107-114

The dynamical behavior of asteroids inside the 2:1 and 3:2 commensurabilities with Jupiter presents a challenge. Indeed most of the studies, either analytical or numerical, point out that the two resonances have a very similar dynamical behavior. In spite of that, the 3:2 resonance, a little outside the main belt, hosts a family of asteroids, called the Hildas, while the 2:1, inside the main belt, is associated to a gap (the Hecuba gap) in the distribution of asteroids.In his search for a dynamical explanation for the Hecuba gap, Wisdom (1987) pointed out the existence of orbits starting with low eccentricity and inclination inside the 2:1 commensurability and going to high eccentricity, and thus to possible encounters with Mars. It has been shown later (Henrard et al.), that these orbits were following a path from the low eccentric belt of secondary resonances to the high eccentric domain of secular resonances. This path crosses a bridge, at moderate inclination and large amplitude of libration, between the two chaotic domains associated with these resonances.The 3:2 resonance being similar in many respects to the 2:1 resonance, one may wonder whether it contains also such a path. Indeed we have found that it exists and is very similar to the 2:1 one. This is the object of the present paper.  相似文献   

The Earth-figure perturbations in the Lunar theory     

J. Henrard 《Celestial Mechanics and Dynamical Astronomy》1981,25(4):417-425

We compute the perturbations on the motion of the Moon due to the shape of the Earth. The zonal terms inJ ₂,J ₃, andJ ₄ are considered. The accuracy is estimated at 3×10^–5 and the results compared with previous theories.  相似文献   

On the artificial satellite theory     

J. Henrard 《Celestial Mechanics and Dynamical Astronomy》1976,14(3):331-331

Some of the basic ideas of an analytical orbiter theory which is being developed by Hubert Claes in Namur are presented.The theory is based on the Lie transform technique and will be expressed in a closed form up to second order. The inclusion of additional terms of the third order (expanded in power series of the eccentricity) will be considered.Special attention is being given to the choice of the elements and to the final form of the theory. Three main criteria are used. The removal of the virtual singularities of small inclination and eccentricity. The simplicity of the final form of the theory once the elements have been given their numerical values. The numerical stability of the evaluation of the theory.  相似文献   

Editorial note     

Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1994,60(1):1-2

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Surfaces of section in the Miranda-Umbriel 3:1 inclination problem     

Michèle Moons  Jacques Henrard 《Celestial Mechanics and Dynamical Astronomy》1994,59(2):129-148

The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermottet al. (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 inclination resonance between Miranda and Umbriel is analysed.  相似文献   

On Brown's conjecture     

J. Henrard 《Celestial Mechanics and Dynamical Astronomy》1983,31(2):115-122

We examine the conjecture made by Brown (1911) that in the restricted three body problem, the long period family of periodic orbits aroundL ₄, ends on a homoclinic orbit toL ₃. By numerical integration we establish that for the mass ratio Sun-Jupiter such a homoclinic orbit toL ₃ does not exist but that there exists a family of homoclinic orbits to periodic orbits aroundL ₃.  相似文献   

Colombo's top     

Jacques Henrard  Charles Murigande 《Celestial Mechanics and Dynamical Astronomy》1987,40(3-4):345-366

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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   

Perturbations by the oblateness of Earth and Moon     

J. Henrard 《Celestial Mechanics and Dynamical Astronomy》1982,26(1):95-95

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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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