RESEARCH ON THE PERIODIC ORBIT OF NON-LINEAR DYNAMIC SYSTEMS USING CHEBYSHEV POLYNOMIALS

Abstract

In this paper, a new analysis method is presented to study the steady periodic solution of non-linear dynamical systems over one period. By using the good properties of Chebyshev polynomials, the state vectors appearing in the equations can be expanded in terms of Chebyshev polynomials over the principal period such that the original non-linear differential problem is simplified to a set of non-linear algebraic equations. Furthermore, all systems, including linear, weak non-linear and strong non-linear can be analyzed in the same way for no limitation of small parameter any more. It is also very efficient to get the asymptotic solution of periodical orbit even for high-dimensional dynamical systems. The numerical accuracy of the proposed technique is compared with that of the standard numerical Runge–Kutta method.