Abstract
The motion of a system of point masses in a negatively uniform force field is investigated. The Lyapunov instability of the Lagrangian configurations of the system, corresponding to constant distances between the points, is established The proof of the instability is based on representing the Lagrangian of the problem in question in a form which enables the Hamilton action to be calculated in explicit form as a function of the phase variables. Problems of the orbital instability of the Lagrangian configurations are discussed.
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