On the dynamical instability in the restricted rectilinear three-body problem

The properties of trajectories of infinitesimal mass are considered in the rectilinear three-body problem. Extensive calculations of such trajectories are performed by numerical integration. The domain of increased sensitivity to initial conditions is obtained that determines the dynamical instability and the possibility of developing chaos in the system. The problem studied simulates, in accordance with chosen initial conditions, the motion of clouds in the Local Group of galaxies.