ar X iv : h ep - t h / 95 05 06 4 v 1 1 1 M ay 1 99 5 Complete integrability for Lagrangian dependent on acceleration in a space – time of constant

The motion equations for a Lagrangian L(k1), depending on the curvature k1 of the particle worldline, embedded in a space–time of constant curvature, are considered and reformulated in terms of the principal curvatures. It is shown that for arbitrary Lagrangian function L(k1) the general solution of the motion equations can be obtained by integrals. By analogy with the flat space–time case, the constants of integration are interpreted as the particle mass and its spin. As examples, we completely investigate Lagrangians linear and quadratic in (k1) and the model of relativistic particle with maximal proper acceleration, in a space–time with constant curvature. PACS: 14.80.Pb 02.40.Hw Ricerca effettuata con i fondi M.U.R.S.T. 40% e 60% art. 65 D.P.R. 382/80. E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected]