WorldCat Identities

Robutel, Philippe

Overview
Works: 15 works in 25 publications in 2 languages and 36 library holdings
Roles: Opponent, Thesis advisor, Author, Other, Contributor
Publication Timeline
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Most widely held works by Philippe Robutel
Contribution à l'étude de la stabilité du problème planétaire des trois-corps by Philippe Robutel( )

3 editions published between 1993 and 2019 in French and held by 6 WorldCat member libraries worldwide

Le but de ce travail est d'obtenir des résultats globaux portant sur la nature des mouvements dans le problème planétaire des trois corps (une étoile et deux planètes). L'étude de la stabilité d'un tel système est abordée suivant deux aspects distincts et complémentaires. Le premier, de nature théorique, se fonde sur une application de la théorie KAM. Après une construction totalement analytique du hamiltonien séculaire obtenue à l'aide d'un manipulateur algébrique, l'application du théorème d'Arnold élaboré en 1963 permet de montrer que presque toutes les conditions initiales conduisent à des trajectoires quasi-périodiques. Ce résultat de stabilité est valable pour des inclinaisons inferieures à un degré et de très faibles masses et excentricités planétaires. Le deuxième aspect de l'étude porte sur la description de la dynamique séculaire des couples planétaires du type Jupiter-Saturne (de masses trop élevées pour être redevables du résultat précèdent). Des méthodes numériques, telle l'analyse en fréquence, montrent que la majeure partie des trajectoires est voisine d'orbites quasi-périodiques, et ce sur un temps comparable à l'âge du système solaire. Une analyse fine (estimation du taux de diffusion) met en évidence que, même au voisinage des résonances séculaires, un tel problème reste très stable. Ainsi il semble qu'en dehors des résonances en moyen-mouvement (qui peuvent nuire considérablement à leur stabilité), les trajectoires de tels systèmes se comportent de manière fortement régulière sur une très longue échelle de temps
Stabilité effective des systèmes planétaires : application au problème séculaire de Jupiter et Saturne by Franck Malige( Book )

3 editions published between 2001 and 2019 in French and held by 4 WorldCat member libraries worldwide

Since the end of the 80's, numerical studies have displayed the appearance of chaotic motion in the trajectories of the planets of our solar system, more precisely of a caracteristical time of sensibility to initial conditions of about 5 million years. This implies the impossibility to foresee the motion of the planets over 100 million years. In such a duration, the planets can even collide. Nevertheless, for the system of outer planets only, these numerical studies have displayed that the chaotic behavior has very little effect during the time of the solar system life. The aim of this thesis is to prove some results of stability for sub-systems of the solar system which numerical study has shown effective stability. We develop rigorous analytical methods to study the stability of the trajectories, that can be used for a general planetary system. We used classical tools : expression of the equations of the motion by means of variables linked to the elliptical elements, secularization, perturbation methods (construction of a Birkhoff normal form at a high degree). A precise study of the constructability of such a normal form is achieved : owing to a degeneracy of the secular problem, we show that this construction cannot be done in general. To solve this problem, we give a new way to reduce partially the n-body planetary problem using the angular momentum integral. Finally, we apply these methods to a system close to reality : the 3-body problem (Sun, Jupiter and Saturn), secular at order one of the mass ratio. We prove a result of stability : the trajectories stay close to a given torus of the phase space for more than 5 milliard years and close to a quasi-periodic solution for about 100 million years
Dynamique fractionnaire pour le chaos hamiltonien by Pierre Inizan( )

3 editions published between 2010 and 2019 in French and held by 4 WorldCat member libraries worldwide

De nombreuses caractéristiques des systèmes hamiltoniens chaotiques, notamment mises en évidence à l'aide de simulations numériques, restent encore mal comprises. Parmi différentes pistes de recherches, Zaslavsky propose une analyse de ces systèmes à l'aide de dérivées fractionnaires. Même si son travail n'est pas complètement formalisé, ses résultats semblent prometteurs. Le calcul fractionnaire permet de généraliser des équations différentielles afin de prendre en compte certains phénomènes complexes. Pour les systèmes lagrangiens et hamiltoniens, le plongement fractionnaire développé par Cresson fournit une procédure basée sur le principe de moindre action pour construire des équations fractionnaires de la dynamique. L'objectif principal de cette thèse est d'utiliser ce formalisme afin de consolider le travail de Zaslavsky. Après avoir présenté quelques éléments sur le calcul fractionnaire, nous enrichissons le plongement fractionnaire en le conciliant avec le principe de causalité et en le rendant dimensionnellement homogène. Nous tentons ensuite de comprendre comment peut émerger une dynamique fractionnaire dans les systèmes hamiltoniens chaotiques, à travers deux pistes respectivement basées sur les travaux de Stanislavsky et Hilfer. Si la première reste problématique, la seconde se concrétise en un modèle simple de dynamique où une dérivée fractionnaire apparaît lorsqu'est prise en compte l'analyse de Zaslavsky. Enfin, en marge de l'étude de ces systèmes, nous montrons que la formulation causale du plongement permet de doter certaines équations dissipatives de structures lagrangiennes fractionnaires, ouvrant ainsi la voie à de nouvelles modélisations numériques
Contribution à l'analyse de la dynamique des troyens : évolution du réseau de résonances en fonction des fréquences planétaires by Julien Bodossian( Book )

3 editions published between 2008 and 2019 in French and held by 3 WorldCat member libraries worldwide

We analyse the evolution of trojan's dynamic when the configuration of the planetary system changes. The triangular equilibrium points are perturbed by the influence of planets. In the first chapter we construct a secular model which gives an analytic approximation of the new equilibrium points under this influence. This work reveals that the inner planets have grower influences than the outer ones. In the second chapter, we study the evolution of the planetary system during the planetary migration. In the third chapter, we classify the resonances which perturb the trojans in four very general families. We also give some methods which predict when they appear in the field of trojans' frequencies. In fourth and fifth chapters, we apply our model in order to study the evolution of Jupiter's and Saturn's trojans dynamic during the planetary migration. During the planetary migration the planetary evolution is very complicated, that's why we decide to work changing only one parameter: Saturn's semi-major axis. We calculate the trajectories of trojans for several values of this parameter. Then we detail the evolution of each family. Our work show that many resonant structures have strongly destabilized Saturn's trojans during the end of planetary migration. As a result, Saturn's trojans have been ejected whereas very few could be captured. On the contrary, Jupiter's trojans are very few destabilized by resonances during the end of the migration, which permit the surviving of numerous trojans. Lastly, we study the dynamic of Neptune's trojans in the actual solar system
Rigorous treatment of the averaging process for co-orbital motions in the planetary problem by Philippe Robutel( )

1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide

On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited by Alexandre Pousse( )

1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide

On the Co-orbital Motion in the Three-Body Problem: Existence of Quasi-periodic Horseshoe-Shaped Orbits by Laurent Niederman( )

1 edition published in 2020 in English and held by 2 WorldCat member libraries worldwide

The chaotic obliquity of the planets by Jacques Laskar( Book )

2 editions published between 1992 and 1993 in English and held by 2 WorldCat member libraries worldwide

Propriétés du système séculaire by Khaled Abdullah( )

2 editions published between 2001 and 2019 in French and held by 2 WorldCat member libraries worldwide

Secular dynamics of multiplanetary circumbinary systems: stationary solutions and binary-planet secular resonance by Eduardo Andrade-Ines( )

1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide

Secular dynamics of S-type planetary orbits in binary star systems: applicability domains of first- and second-order theories by Eduardo Andrade-Ines( )

1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide

Stability of the planetary three-body problem I. Expansion of the planetary Hamiltonian by Jacques Laskar( )

1 edition published in 1995 in English and held by 2 WorldCat member libraries worldwide

Dynamique des planètes coorbitales by Adrien Leleu( )

1 edition published in 2016 in French and held by 1 WorldCat member library worldwide

Ce travail porte principalement sur la dynamique et les méthodes de détection des exoplanètes coorbitales. Nous appelons "coorbitale" toute configuration pour laquelle deux planètes orbitent avec le même moyen mouvement moyen autour d'une même étoile. Dans un premier temps, nous revisitons les résultats du cas coplanaire circulaire. Nous rappelons également que les variétés des coorbitaux circulaires et celle des coorbitaux coplanaires sont toutes deux invariantes par le flot du Hamiltonien moyen. Nous nous intéressons donc à ces deux cas particuliers. L'accent est mis sur le cas coplanaire (excentrique), où nous étudions l'évolution de familles d'orbites quasi-périodiques de dimension non maximale en fonction de l'excentricité des planètes. Nous montrons que la géométrie des ces familles dépend fortement de l'excentricité, ce qui entraine des changements de topologie importants dans l'ensemble de l'espace des phases à mesure que celle-ci augmente. Un chapitre est dédié à la détection des exoplanètes coorbitales. On y rappelle les différentes méthodes de détection adaptées au cas coorbital. On développe particulièrement le cas des vitesses radiales, ainsi que leur combinaison avec des mesures de transit. Enfin, on décrit une méthode permettant d'étudier l'effet de perturbations orbitales sur les résonances spin-orbite d'un corps indéformable. Nous appliquons cette méthode dans deux cas: le cas coorbital excentrique, et le cas circumbinaire
The Moon : a climate regulator for the Earth by Jacques Laskar( Book )

1 edition published in 1992 in English and held by 1 WorldCat member library worldwide

Le quasi-satellites et autres configurations remarquables en résonance co-orbitale by Alexandre Pousse( )

1 edition published in 2016 in French and held by 1 WorldCat member library worldwide

This work of thesis focuses on the study of the coorbital resonance. This domain of particular trajectories, where an asteroid and a planet gravitate around the Sun with the same period possesses a very rich dynamics connected to the famous Lagrange's equilateral configurations L4 and L5, as well as to the Eulerian's configurations L1, L2 and L3. A major example in the solar system is given by the “Trojan” asteroids harboured by Jupiter in the neighborhood of L4 and L5. A second astonishing configuration is given by the system Saturn-Janus-Epimetheus; this peculiar dynamics is known as “horseshoe”. Recently, a new type of dynamics has been highlighted in the context of co-orbital resonance: the quasi-satellites. They correspond to remarkable configurations : in the rotating frame with the planet, the trajectory of the asteroid seems the one of a retrograde satellite. Some asteroids harboured by Venus, Jupiter and the Earth have been observed in this kind of configuration. The quasi-satellite dynamics possesses great interest not only because it connects the different domains of the co-orbital resonance (see works of Namouni, 1999), but also because it seems to bridge the gap between satellization and heliocentric trajectories. However, despite the term quasi-satellite has become dominant in the celestial mechanics community, some authors rather use the term “retrograde satellite”. This reveals an ambiguity on the definition of these trajectories. For these reasons, the first part of this thesis consisted in clarifying the definition of these orbits by revisiting the planar-circular case (planet on circular motion) in the framework of the averaged problem. In the second part of this thesis, we developed an analytic method to explore the quasi-satellite domain in the averaged problem. We realized this exploration in the planar-circular case and proposed an extension to the planar-eccentric and spatial-circular cases. The recent discoveries around the exo-planets motivated some works on the co-orbital resonance in the planetary Three-Body Problem. In this context, Giuppone et al. (2010) highlighted (numerically) the quasi-satellite as well as new families of remarkable configurations: the “anti-Lagrange”. Then the third part of this thesis presents an analytical method for the planetary problem that allows to reveal the anti-Lagrange orbits as well as a sketch of study of quasi-satellite trajectories
 
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Audience level: 0.95 (from 0.92 for Stabilité ... to 1.00 for Dynamique ...)

Associated Subjects
Languages
French (16)

English (9)