Abstract
The stability of periodic motion is studied in the critical case of n pairs of purely imaginary characteristic indices. It is shown that in the case of resonance, when the ratio of the modulus of one of the characteristic indices to the frequency of the unperturbed motion is an integer, instability usually occurs. The results obtained are used to study the free oscillations of an autonomous quasilinear system when the Andronov-Witt criterion /1/ cannot be used. The instability of free oscillations of the Froude pendulum at the bifurcation point is proved.
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