Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem

We consider the situation when three heavy gravitational bodies form the Lagrange conÖguration rotating in a fixed plane and the fourth body of negligible mass moves in this plane. We present three cases of so-called libration points and we study their stability using linear approximation and the KAM theory. In some situations we prove the Lyapunov stability for generic values of some parameter of the problem.