Normal Form Solution of Reduced Order Oscillating Systems

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamic systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. Such a system is reduced into its centre manifold before computation of normal forms, which are obtained using a period averaging method applicable to 71071autonomous systems and more advantageous than the classical methods. A good agreement was observed between the predicted results from the normal form theory and the numerical simulations of the original system.