Motion in the generalized restricted three-body problem

This paper investigates the motion of an infinitesimal body in the generalized restricted three-body problem. It is generalized in the sense that both primaries are radiating, oblate bodies, together with the effect of gravitational potential from a belt. It derives equations of the motion, locates positions of the equilibrium points and examines their linear stability. It has been found that, in addition to the usual five equilibrium points, there appear two new collinear points Ln1, Ln2 due to the potential from the belt, and in the presence of all these perturbations, the equilibrium points L1, L3 come nearer to the primaries; while L2, L4, L5, Ln1 move towards the less massive primary and Ln2 moves away from it. The collinear equilibrium points remain unstable, while the triangular points are stable for 0<μ<μc and unstable for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mu_{c} \le\mu\le\frac{1}{2}$\end{document}, where μc is the critical mass ratio influenced by the oblateness and radiation of the primaries and potential from the belt, all of which have destabilizing tendency. A practical application of this model could be the study of the motion of a dust particle near the oblate, radiating binary stars systems surrounded by a belt.