On the phase-plane analysis of non-linear time-varying systems

A phase plane technique, which takes advantage of convenient relationships in other planes (for example, displacement versus time) to effect graphical solutions for a non-linear time varying second order differential equation, is developed. Several special cases of this general second order equation are considered. The special case of most practical importance occurs when the differential equation is permitted to become piece-wise linear. To demonstrate the simplicity of the technique, for the piecewise linear case, an example involving saturation in an inertially damped position servomechanism is given.