Stability of the equilibrium solutions in a charged restricted circular three-body problem

• We study a charged three-body problem.
• We give a complete study of the Lyapunov stability of the isosceles equilibria.
• We give a complete study of the Lyapunov stability of the collinear.
• We have different types of resonances.
• We study some critical and degenerate cases.

In this paper we describe a charged restricted circular three-body problem (CHRCTBP). Then, the particular equilibrium points, namely, the collinear equilibrium points L1coll, L2coll and L3coll and the isosceles triangle equilibrium L4iso and L5iso are characterized in an explicit way as functions of the parameters μ (parameter associated with the mass of the primaries) and β (parameter associated with the charges). The linear stability of each planar solution is studied and the curves of resonance are analyzed. Finally, the Lyapunov stability (nonlinear) is provided in each of these equilibrium solutions.