Phase-Plane Graphics—A New Approach to Teaching Dynamics

The theory of the phase plane is briefly presented in Part I, and three basic phase-plane trajectories are derived to acquaint the reader with the techniques of phase-plane plotting. Graphical analysis on the phase plane is proposed as a teaching aid for undergraduate courses in mechanics and vibration. In Part II the laws of elementary impact are reviewed and a concise phase-plane representation of impact is derived from the impact equations. The phase-plane method is used to study the motion resulting from the impact between two equal period pendulums of 3-to-1 mass ratio. Advantages of the phase-plane representation of impact are cited. In Part III the basic phase-plane trajectories derived in Part I are used as components of exact phase-plane representations of various discontinuous motions, such as dissipative impact of two mass particles and dissipative bouncing.