Parametric resonance with a nonlinear term: Comparison of averaging and the normal form method using a simple example
Résumé
The principal resonance of the Mathieu differential equation with an additional cubic term is investigated. First order averaging and the normal form method are applied to calculate approximately the amplitude of the resulting oscillation. For both methods unimportant variants in the detail lead to qualitatively different results. These are compared to numerical calculations using the shooting method.