  For the relativistic string with massive ends arbitrary small disturbances of
the uniform rotation of the rectilinear string are investigated. There are two
classes of these oscillations with different spectra of frequencies. They are
stationary waves oscillating in the rotational plane and in the orthogonal
direction. These states are presented in the form of Fourier series that helps
to quantize string excitations in the linear vicinity of the classical
rotation. These string oscillations may be applied to describing daughter Regge
trajectories in the framework of the considered model
