Chargé de recherches

The higher order effects of a full lunar gravitational field on the dominating forces on a spacecraft in the vicinity of the moon are investigated. The long term behavior becomes apparent after a first order averaging that removes the spacecraft's mean anomaly and argument of the node. Recurrence equations for the averaged flow in the eccentricity and the argument of perilune are built upon prior recurrences by one of the authors that avoid the need of computing quadratures. Zeros of the reduced flow, which are easily found by means of root-finding procedures, represent higher-order solutions to the frozen orbit problem. These frozen orbits have the argument of perilune either at 90 or 270 deg., depending on inclination, and may hold low eccentricities. Having available analytical equations, the computation of frozen orbits' eccentricity-inclination diagrams is almost inexpensive, and reveals the minimum eccentricity orbits commonly required in preliminary mission design.

There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronization phenomenon. Here, we identify the type of such synchronization and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the Van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal, the traditional concepts of phase-or frequency-locking used to define synchronization to periodic forcing are inadequate. Instead, we explore a different concept of generalized synchronization in terms of (coexisting) synchronized solutions for the forced system, their basins of attraction and instabilities.

There is wide evidence and acceptation that ice age cycles are paced by changes in the seasonal and spatial distributions of insolation, induced by variations in the astronomical elements of planet Earth. However, the usual concept of phase-locking is reserved for periodic forcings. Here, we introduce the cardinality of the pullback attractor as a useful measure of synchronisation in the context of a quasi-periodic forcing, such as the astronomical forcing. The concept is illustrated with a small palaeoclimate model akin of the celebrated Van der Pol oscillator. At low forcing amplitude the system may lock on the individual components of the astronomical forcing in a way that is similar to phase-locking on periodic forcing, but as the amplitude is increased the combined effects of precession and obliquity restrict the number of possible climate histories. We describe a phenomenon similar to the 'phase-slip' encountered in periodic-forced systems subject to additive fluctuations and comment on its relevance and consequences at palaeoclimate time scales.

We are currently developing an analytical theory of an artificial satellite of the Moon. It is an interesting problem because the dynamics of a lunar orbiter is quite different from the one of an artificial satellite of the Earth, by at least 2 aspects: the C22 lunar gravity term is only 1/10 of the J_2 term and the third body effect of the Earth on the lunar satellite is much larger than the effect of the Moon on a terrestrial satellite. So we have to account at least for these larger pertubations. We use here the method of the Lie Transform as perturbation method. The Hamiltonian of the problem is first averaged over the fast angle, in canonical variables. The solution is developped in powers of the small factors linked to n (the mean motion of the moon), J_2, C22 and to the Earth's position. The Earth location is determined by the lunar theory ELP2000 [Chapront, J. and Chapront-Touzé] from which we take the leading terms. Series development are made with our home-made Algebraic Manipulator, the MM (standing for "Moon's series Manipulator"). The results are obtained in a closed form, without any series developments in eccentricity or inclination. So the solution apply for a wide range of values, except for few isolated critical values. We achieved a.o. second order results for the combined effect of J_2 and C22. As a side result, we were able to check the second order generator W2 given by Kozai for the effect of the J_2 term on an artificial satellite.

The higher order effects of a full lunar gravitational field on the dominating forces on a spacecraft in the vicinity of the moon are investigated. The long term behavior becomes apparent after a first order averaging that removes the spacecraft’s mean anomaly and argument of the node. Recurrence equations for the averaged flow in the eccentricity and the argument of perilune are built upon prior recurrences by one of the authors that avoid the need of computing quadratures. Zeros of the reduced flow, which are easily found by means of root-finding procedures, represent higher-order solutions to the frozen orbit problem. These frozen orbits have the argument of perilune either at 90 or 270 deg., depending on inclination, and may hold low eccentricities. Having available analytical equations, the computation of frozen orbits’ eccentricity–inclination diagrams is almost inexpensive, and reveals the minimum eccentricity orbits commonly required in preliminary mission design.

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DI-fusion, le Dépôt institutionnel numérique de l'ULB, est l'outil de référencementde la production scientifique de l'ULB.L'interface de recherche DI-fusion permet de consulter les publications des chercheurs de l'ULB et les thèses qui y ont été défendues.

O vir venerande Wibalde, Stabulensis ecclesie abba, meritorum fama futuris seculis recolende Ô vénérable Wibald, abbé de l'église de Stavelot, [toi] qui mérite d'être honoré par les siècles futurs en raison de la renommée de tes mérites 1153 - Charte de Frédéric Barberousse à Wibald, abbé de Stavelot 1

DI-fusion, le Dépôt institutionnel numérique de l'ULB, est l'outil de référencementde la production scientifique de l'ULB.L'interface de recherche DI-fusion permet de consulter les publications des chercheurs de l'ULB et les thèses qui y ont été défendues.

DI-fusion, le Dépôt institutionnel numérique de l'ULB, est l'outil de référencementde la production scientifique de l'ULB.L'interface de recherche DI-fusion permet de consulter les publications des chercheurs de l'ULB et les thèses qui y ont été défendues.

DI-fusion, le Dépôt institutionnel numérique de l'ULB, est l'outil de référencementde la production scientifique de l'ULB.L'interface de recherche DI-fusion permet de consulter les publications des chercheurs de l'ULB et les thèses qui y ont été défendues.