Unstable Rotational States of Closed String with Massive Points

For the closed string carrying 2 or 3 point-like masses the stability problem for central and linear rotational states is considered. This problem is important for applications of these model to describing baryons, glueballs or other exotic hadrons. The linear rotational state correspond to an uniform rotation of the system with rectilinear string segments, connecting massive points. The state is named “central” one, if there is a massive point at the rotational center. It is shown that the linear rotational states with 2 massive points are stable with respect to small disturbances. But the central rotational states with 3 masses are not stable, if the central mass it less than energy of the string with other massive points. This effect may change properties of excited hadron states, in particular, increase their width.