Computation of the coefficients associated with the normal form of a resonant five-dimensional system

In this paper, normal forms and the related coefficients associated with a five-dimensional resonant nonlinear system are investigated. It is assumed that the linearized system has two pure imaginary pairs and a zero eigenvalue. A modified normal form method is applied to a resonant model 1 : 2; however, the ideas presented here can be applied to other resonant models, as well. A symbolic computer language, MAPLE, has been used to obtain most of the results.