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Normal form computation without central manifold reduction

A. Leung
Organization: City University of Hong Kong
Q. C. Zhang
Organization: Tiianjin University
Department: School of Mechanical Engineering
Journal / Anthology

Journal of Sound and Vibration
Year: 2003
Volume: 266
Issue: 2
Page range: 261-279

An efficient method for calculating the normal form and the associated non-linear transformations for the semi-simple case without central manifold reduction is given in this paper. The one-step transformation concept is adopted for easy programming. This method can be used to calculate high order normal forms of high-dimensional ordinary differential equations of non-linear oscillators. A program in MATHEMATICA language is designed to perform the calculation. Three examples are given in order to verify the method and to show the efficiency of the program.

*Mathematics > Calculus and Analysis > Differential Equations