ABSTRACT
Linear system analysis serves to explain much of the behavior of oscillatory systems. However, there are a number of oscillatory phenomena that cannot be predicted or explained by the linear theory. The perturbation method is applicable to problems in which a small parameter µ is associated with the nonlinear term of the differential equation. The solution is formed in terms of a series of the perturbation parameter µ, the result being a development in the neighborhood of the solution of the linearized problem. Self-excited oscillations may occur in a linear or a nonlinear system. The motion is induced by an excitation that is some function of the velocity or of the velocity and the displacement. If the motion of the system tends to increase the energy of the system, the amplitude will increase, and the system may become unstable.
