On periodic solutions of parametrically excited complex non-linear dynamical systems

An approximate analytical method, based on the generalized averaging method is extended to study periodic solutions of parametrically excited complex non-linear dynamical systems. It is well known that a great many problems of applied sciences often lead to the study of these dynamical systems. Our analytical approach provides us with specific values for the parameters of these dynamical systems for which such periodic solutions exist. An example which is related to rotor dynamics and spherical pendulum with vertically oscillating support is considered to illustrate this approach. Analytical results on this example are compared with numerical ones and excellent agreement is found between them.