Vibrational modes of a rotating string

Abstract

Motivated by nonrelativistic models of a QCD (quantum chromodynamic) string, we examine the systemof a nonrelativistic string in uniform rotational motion with one endfixed and with a mass (quark) attached to the other end. A QCD string hasno purely longitudinal modes, so some constraint must be imposed upon thenonrelativistic system to exclude these modes. Accordingly, we examinethe cases that the string is either inextensible or purely transverse. Foreach case we solve first the discretized string and then do the continuumcase. We find the small amplitude oscillatory motions and frequencies ofoscillation of the string and mass. We show that the assumption of a nodeat the end of the inextensible string produces frequencies that are veryclose to the actual frequencies. For the transverse string, we show thatkeeping centrifugal terms for the motion of the masses comprising thestring leads to an unstable mode.PACS Nos.: 03.20.+i, 03.40.-t, 12.39.Mk