Abstract
Conservative non-linear systems with two degrees of freedom that allow of normal vibrations with rectilinear trajectories in configuration space are examined. The normal vibrations of non-linear systems are a generalization for normal (principal) vibrations of linear systems/1/. The value of such solutions is determined by the fact that the resonance modes are close to normal vibrations for small external periodic effects. A number of recent papers (/2–5/etc.) are devoted to the analysis of normal vibrations. Within the framework of the stability problem to a first approximation, or normal vibrations, conditions are obtained for which the number of instability zones in the system parameter space is finite. The eigenfunctions and eigenvalues corresponding to the zone boundaries are determined.
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