Some techniques for order reduction of nonlinear time periodic systems

In this paper, some techniques for order reduction of nonlinear systems with time periodic coefficients are introduced. The equations of motion are first transformed using the Lyapunov-Floquet transformation such that the linear parts of the new set of equations are time-invariant. To reduce the order of this transformed system three model reduction techniques are suggested. The first approach is simply an application of the well-known linear method to nonlinear systems. In the second technique, the idea of singular perturbation and nonlinear projection are employed, whereas the concept of invariant manifold for time-periodic system forms the basis for the third method.