For the relativistic string with massive ends, the three-string baryon modeland other string models of the baryon the small disturbances of well knownrotational motions are considered. For the string meson model the two types ofthese disturbances (quasirotational motions) are obtained. They are oscillatorymotions in the form of stationary waves in the rotational plane and in theorthogonal direction. These solutions may be used for describing more widespectrum of hadron excitations and for the quantization of this nonlinearsystem. For three-string baryon model or Y configuration these quasirotationalmotions are more complicated and contain the branch with growing amplitudes.This consideration proves that for the three-string model with both masslessand massive ends the rotational motions are unstable on the classical level.
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