THE INSTABILITY OF LAGRANGIAN CONFIGURATIONS OF ATTRACTING POINT MASSES

The motion of a system of point masses in a negatively uniform force f ield is investigated. The Lyapunov instability of the Lagrangian confi gurations of the system, corresponding to constant distances between t he points, is established. The proof of the instability is based on re presenting the Lagrangian of the problem in question in a form which e nables the Hamilton action to be calculated in explicit form as a func tion of the phase variables. Problems of the orbital instability of th e Lagrangian configurations are discussed. Copyright (C) 1996 Elsevier Science Ltd.