Curved QCD string dynamics

We consider the effects of going beyond the approximation of a straight string in mesons by using a flexible flux tube model wherein a Nambu-Goto string bends in response to quark accelerations. The curved string is dynamically identical to the straight string even for ultra-relativistic mesons except for a small additional radial momentum. We numerically solve the curved string model in the case where both ends have equal mass quarks and also in the case where one end is fixed. No approximation of non-relativistic motion is made. We note some small but interesting differences from the straight string. {copyright} {ital 1999} {ital The American Physical Society}