Analysis of Non-linear Differential Equations by the Volterra Series†

Abstract

The Volterra series is used to investigate aperiodic solutions of certain second-order differential equations with non-linear damping and non-linear restoring force. Solutions are obtained in the phase plane for trajectories with zero initial conditions. These are obtained by approximating the Volterra series, and it is shown that the approximation involved is small over a wide range of values of linear damping.