A field method and its application to the theory of vibrations (Q1058323)

A field method for solving a system of ordinary differential equations of motion of a nonconservative dynamical system is presented in the paper. The basic idea is that instead of trying to find the solution of the original system directly an equivalent quasi-linear partial differential equation of the first order is constructed. The complete integrals have been obtained for these equations. The concept of the complete solution has been applied to the nonlinear vibration problems, combining the method described in the paper with the well known asymptotic method of the dual time expansion. Two examples of nonlinear one-degree-of-freedom oscillators (the Van der Pol oscillator and the Duffing oscillator) are presented in the last part of the paper which should be of interest to researchers in the field of nonlinear vibrations.