L'équation aux variations verticales d'un équilibre relatif comme source de nouvelles solutions périodiques du problème des N corps

We start with a rotating frame which enforces a resonance between the frequency of a relative equilibrium of the N-body problem and that of an infinitesimal variation normal to the plane of the equilibrium. Continuation then yields a remarkable class of periodic solutions. The first example is the P12 family, discovered by Christian Marchal, which links the relative equilibrium of Lagrange to the Eight. To cite this article: A. Chenciner, J. Féjoz, C. R. Acad. Sci. Paris, Ser. I 340 (2005).