DYNAMICS OF RELATIVISTIC-PARTICLES WITH LAGRANGIANS DEPENDENT ON ACCELERATION

Models of relativistic particles with Lagrangians L(k(1)), depending o n the curvature of the worldline k(1), are considered. By making use o f the Frenet basis, the equations of motion are reformulated in terms of the principal curvatures of the worldline. It is shown that for arb itrary Lagrangian function L(k(1)) these equations are completely inte grable, i.e., the principal curvatures are defined by integrals. The c onstants of integration are the particle mass and its spin. The develo ped method is applied to the study of a model of a relativistic partic le with maximal proper acceleration, whose Lagrangian is uniquely dete rmined by a modified form of the invariant relativistic interval. This model gives us an example of a consistent relativistic dynamics obeyi ng the principle of a superiorly limited value of the acceleration, ad vanced recently. (C) 1995 American Institute of Physics.