Abstract
The paper presents a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the necessary and sufficient conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of the motion. Using a method developed by the first author, we obtained the canonical equations of motion, the simplest possible equations. This method is based on the normal forms of the vector fields and it is presented here in a particular case. Finally a complete solved numerical application is presented.
Keywords: normal form, non-linear equations, stability, cubic non-linearity, multi degrees of freedom