NORMAL FORM SOLUTION OF REDUCED ORDER OSCILLATING SYSTEMS

A.   Sedaghat

Department of Mechanical Engineering

Isfahan University of Technology, Isfahan, Iran

E-mail: Sedaghat@cc.iut.ac.ir

Abstract

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations were determined for a simple two-degrees-of-freedom double pendulum system. The double pendulum system was reduced into its centre manifold before applying normal form computations. Normal forms were obtained using a period averaging method which is applicable to non-autonomous systems, more advantageous than the classical methods. Good agreement was obtained between the predicted results from the normal form theory and numerical simulations of the original system.

Keywords: Normal Form Theory, Period Averaging, Limit Cycle Oscillations.