Complete integrability for Lagrangians dependent on acceleration in a spacetime of constant curvature

Abstract

The motion equations for a Lagrangian , depending on the curvature of the particle world line, embedded in a spacetime of constant curvature, are considered and reformulated in terms of the principal curvatures. It is shown that, for an arbitrary Lagrangian function , the general solution of the motion equations can be obtained by integrals. By analogy with the flat spacetime case, the constants of integration are interpreted as the particle mass and its spin. As examples, we completely investigate Lagrangians linear and quadratic in and the model of a relativistic particle with maximal proper acceleration, in a spacetime with constant curvature.