On the Stability of Collinear Libration Points in the Three-Body Problem with Two Radiating Masses

Abstract

The stability of cloud accumulations of gas and dust particles in the field of binary star systems is studied. As a dynamic model, we consider a restricted three-body problem in which both main bodies are radiating. We study the stability of collinear libration points (CLL) in a nonlinear formulation. The problem of CLP stability is considered in three-dimensional parametric space. It is shown that at the resonance of the fourth order in the plane problem, the points under study are stable in the sense of Lyapunov. In this case, the invariant normal form and Markeev’s theorem are used. The stability of the CLP in the spatial problem is considered. The Birkhoff normal form is used and the Arnold–Moser theorem is used. Results are obtained on stability for most initial conditions (in the Lebesgue measure) and formal stability.

Keywords

• collinear libration points
• gravity
• resonance
• stability
• field
• radiating