On a problem of a field method and its applications to the non-linear vibrations

In this paper the integration of the differential equations of motion of a non-conservative dynamical system is replaced by an equivalent problem of finding a complete integral a quasi-linear partial differential equation of the first order. In second part, these complete integrals are combined with the two time scales perturbation method in the study of non-linear oscillatory motions. [Copyright &y& Elsevier]