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The relativistic string equation is solved for motion corresponding to rigid body rotation about the z-axis. One class of these solutions, namely the planar solutions, allows for the construction of two types of exotic meson and one type of glueball, all of which have asymptotically straight Chew-Frautschi plots. The first type of meson only exists when the number of quarks or antiquarks is 4, 5, 6 or 7, whereas no such restriction applies to the second type. For each of these cases the firstdoi:10.1071/ph820223 fatcat:exym72z3wrbpji7uzx4fm2lmf4