COMPLETE-INTEGRABILITY FOR LAGRANGIANS DEPENDENT ON ACCELERATION IN ASPACETIME OF CONSTANT CURVATURE

The motion equations for a Lagrangian L(k(1)), depending on the curvat ure k(1) of the particle world line, embedded in a spacetime of consta nt curvature, are considered and reformulated in terms of the principa l curvatures. It is shown that, for an arbitrary Lagrangian function L (k(1)), the general solution of the motion equations can be obtained b y integrals. By analogy with the flat spacetime case, the constants of integration are interpreted as the particle mass and its spin. As exa mples, we completely investigate Lagrangians linear and quadratic in ( k(1)) and the model of a relativistic particle with maximal proper acc eleration, in a spacetime with constant curvature.