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Article
Étude topologique générale des équations différentielles conservatives (indépendantes du temps ou périodiques). Application à la mécanique céleste
Les systèmes d'équations différentielles conservatives (indépendants du temps ou périodiques) sont très courants, par example ceux mis sous la forme canonique deHamilton et dont l'Hamiltonien est suffisamment rég...
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Article
The quasi integrals
The usual Von Zeipel transformations of the Hamiltonian Mechanics are presented, they lead to state functions with extremely slow variations: the ‘quasi-integrals’.
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Article
On quasi-integrable problems. The example of the artificial satellites perturbed by the Earth's zonal harmonics
With the Hamiltonian parameters developed for the two-fixed-centers problem a simple and very accurate expression of the ‘quasi-integral’ can be given for the motion of artificial satellites perturbed by the E...
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Article
A small example of Arnold diffusion
The Arnold diffusion occurs in the vicinity of most linearly stable solutions of non-integrable autonomous Hamiltonian systems with more than two degrees of freedom. This diffusion is an extremely slow phenome...
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Article
The mystery of Pluto's mass
After a short presentation of the Pluto-Charon system and the history of its mass determinations some first reasons are presented that support the existence of a ring of billions of small satellites about Plut...
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Article
The Family P12 of the Three-body Problem – The Simplest Family of Periodic Orbits, with Twelve Symmetries Per Period
A beautiful plane eight-shaped orbit has been found by Alain Chenciner, Richard Montgomery and Carles Simo through the minimisation of the action between suitable limit conditions. The three masses are equal a...
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Article
How the Method of Minimization of Action Avoids Singularities
The method of minimization of action is a powerful technique of proving the existence of particular and interesting solutions of the n-body problem, but it suffers from the possible interference of singularities....
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Article
The General Solution of the Planar Laplace Problem
The famous Laplace problem is the three-body, secular, planetary problem. Its plane version has the great theoretical advantage of being integrable (Ferraz-Mello, private correspondence, 2001) and Ferraz-Mello...
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Article
Long term evolution of quasi-circular Trojan orbits
Trojan asteroids undergo very large perturbations because of their resonance with Jupiter. Fortunately the secular evolution of quasi circular orbits remains simple—if we neglect the small short period perturb...