Quasirotational Motions and Stability Problem in Dynamics of String Hadron Models

For the relativistic string with massive ends (the meson model) and four various string baryon models (q-qq, q-q-q, Y and $\Delta$) we consider the classical quasirotational motions, which are small disturbances of the planar uniform rotations of these systems. For the string meson model the two types of these solutions are obtained. They describe oscillatory motions in the form of stationary waves in the rotational plane and in the orthogonal direction. This approach and the suggested method of determining an arbitrary motion of the system on the base of initial data let us solve the stability problem for the rotational motions for all mentioned string configurations. It is shown that the classic rotational motions are {\it stable} for the string meson model (or its analog q-qq) and for the $\Delta$ baryon configuration, but they are {\it unstable} for the string baryon models Y and q-q-q. For the latter two systems any small asymmetric disturbances grow with growing time. The motion of the q-q-q configuration become more complicated and quasiperiodic but quarks do not merge. In the case of Y model the evolution of disturbances results in falling a quark into the junction. These features of the classic behavior are important for describing the hadron states on the Regge trajectories and for choosing and developing the most adequate QCD-based string hadron models.