Synthesis approach to the study of a class of nonlinear systems

Solutions to the governing differential equations of certain classes of 2nd-order nonlinear nonautonomous systems are sought in terms of the powers of trigonometric functions with time-varying amplitudes and frequencies. Use of such generating functions in the synthesis of nonlinear systems is justified by the fact that having powers of the trigonometric functions is equivalent to having terms of higher harmonics in the solution, which, of course, is a well known approach in nonlinear-system analysis.