Stability of triangular libration points in the restricted three body problem when both the primaries are triaxial rigid bodies (Q1611447)

The motion of an infinitesimal mass in the three-body problem when both primaries are triaxial rigid bodies is considered. It is assumed that the primaries have axes of symmetry but their equatorial planes do not coincide with the plane of their motion and additionally the principal axes of the primaries are oriented to the synodic axes with the help of Euler's angles. The rigid bodies move around their center of mass without rotation. In a previous article of the authors [Indian J. Pure Appl. Math. 32, No. 1, 125--141 (2001; Zbl 0998.70009)] the existence of displaced libration points for different combinations of shapes of the primaries was proved. The displacements of the libration points depend on two small oblateness factors. In the paper under review the stability of the displaced libration points of the planar restricted three-body problem when the two primaries are triaxial rigid bodies is considered. The case when the primaries are nearly spherical is studied in detail. As in the classical three-body (points) problem, the collinear libration points are unstable and the triangular libration points (displaced, of course) are stable when the mass parameter \(\mu\) satisfies \(0 \leq \mu < \mu_{\text{crit}}\). In this connection the critical parameter \(\mu_{\text{crit}}\) differs from that of the classical three-body problem by a quantity proportional to the small oblateness factors.