Techniques for Analysis of Certain Nonlinear Systems

This paper suggests the use of simple transformations like ẋ=kx, kx
²
for second-order nonlinear differential equations to effect rapid plotting of the phase-plane trajectories. The method is particularly helpful in determining quickly the trajectory slopes along simple curves in any desired region of the phase plane. New planes such as the tẋ-x, tẋ
²
-x are considered for the study of some groups of nonlinear time-varying systems. Suggestions for solving certain higher-order nonlinear systems are also made.