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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...

    C. Marchal in Celestial Mechanics and Dynamical Astronomy (2009)

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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...

    C. Marchal in Celestial Mechanics and Dynamical Astronomy (2005)

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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....

    C. Marchal in Celestial Mechanics and Dynamical Astronomy (2002)

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    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...

    C. Marchal in Celestial Mechanics and Dynamical Astronomy (2000)

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    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...

    C. Marchal in Celestial Mechanics and Dynamical Astronomy (1993)

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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...

    C. Marchal, F. Rannou-Montigny in Celestial mechanics (1987)

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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...

    C. Marchal in Celestial mechanics (1986)

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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’.

    C. Marchal in Celestial mechanics (1980)

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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...

    C. Marchal in Celestial mechanics (1971)