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We investigate classical strings defined by the Nambu-Goto action with theboundary term added. We demonstrate that the latter term has a significantbearing on the string dynamics. It is confirmed that new action terms thatdepend on higher order derivatives of string coordinates cannot be consideredas continuous perturbations from the starting string functional. In the casethe boundary term reduces to the Gauss-Bonnet term, a stability analysis isperformed on the rotating rigid string solution. We determined the most genericsolution that the fluctuations grow to. Longitudinal string excitations arefound. The Regge trajectories are nonlinear.Comment: 9 LaTeX pages and 3 PostScript figures (uuencoded), preprint  TPJU-15/9

Boundary terms in the Nambu-Goto string action