The Dynamics of Lagrangiens Systems with Acceleration Dependence. Part 3

The classical and relativistic one-particle Lagrangiens depend on position and velocity of this particle only. In the publications of the last years were proposed more general forms of Lagrangiens with acceleration-dependence. Such Lagrangiens lead to the Euler-Lagrange equations of motion which have a form of complex non-linear equation of a singular type because a small parameter is a multiplier in front of the highest derivative. In the present publication we study the solutions corresponding to a free motion, and a motion in the external field with the oscillator potential.