Higher order normal form and period averaging

Abstract

Calculation of the higher order averaging equations of a non-linear oscillator is very tedious using the classical averaging method. This is also true for higher order normal forms. This paper presents an alternative method, which is a combination of the method of normal form and the classical averaging method. A simple and efficient program is given to calculate the higher order averaging equations by using the symbolic computer algebra system Mathematica. Furthermore, the program can be used to calculate the higher order coefficients of normal form. Four examples are given and compare well with the existing results.