Mouvements rigides associés à des masses positives et négatives

The Note deals with rigid solutions of the N-Body Problem, i.e. solutions with constant mutual distances between the bodies. It is shown that for these motions, the configuration is balanced in the sense of Albouy and Chenciner [Invent. Math. 131 (1998) 151-184] even when the masses are of different signs. This fact was proved only for positive masses, using the scalar product they define. A consequence of the result is the constancy of the rotation velocity. It is also shown that any configuration can generate non-planar rigid motions for certain masses. Such motions do not exist with positive masses. All the results can be generalized to systems with N charged particles. To cite this article: M. Celli, C. R. Acad. Sci. Paris, Ser. I 340 (2005).