Ligęza A., Żołądek H.
Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem
2021, Vol. 17, no. 4, pp. 369-390
We consider the situation where three heavy gravitational bodies form the Lagrange configuration 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 KAM theory. In some situations we prove the Lyapunov stability for generic values of some parameter of the problem.