Linear stability of elliptic relative equilibria of restricted four -body problem

In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problem where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincare map is decomposed to the essential part, the Keplerian part and the elliptic Lagrangian part where the last two parts have been studied in literature. The linear stability of the essential part depends on the masses parameters alpha, beta and the eccentricity e is an element of [0, 1). Via omega-Maslov index theory and linear differential operator theory, we obtain the full bifurcation diagram of linearly stable and unstable regions with respect to alpha, beta and e. Especially, two linearly stable sub-regions are found. (C) 2020 Elsevier Inc. All rights reserved.