On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined, and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice of the numerical solvers. When the equilibrium states are known certain linearizations around one chosen state may be applied carefully in order to facilitate or speed up the numerical solution of the dynamical problem. It is argued, however, that certain problems cannot be linearized. The applications of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed.