Basic principles of vehicle dynamics

Vehicle dynamics, as its name suggests, is the application of multibody system dynamics to vehicles. But in this sense, it is customary to restrict the term vehicle to unguided land motor vehicles. Thus, in this article, neither rail vehicles nor aircraft will be discussed, even if the latter, when taxiing on the runway, fall into this category. This does not mean, however, that certain theoretical aspects are not related, or that the form of the equations is not similar - just refer to the equations of flight dynamics, for example.

If we return to the definition and application of multi-body system dynamics, we understand that we need to follow the logic of this discipline, i.e. build a multi-body kinematic model of the vehicle, parameterize it, be able to calculate the kinetic elements, but above all determine the external mechanical actions acting on the system. This last point means being able to express these actions as a function of parameters, using theoretical and/or experimental models.

In recent years, a new direction in vehicle dynamics has been emerging, known as "global chassis control". These aids, using data from sensors located in the vehicle and simulation results from vehicle modeling, act on actuators – brakes, steering, suspension, etc. – to help the driver in tricky situations. The choice of actuators, the order, duration and intensity of their intervention, and taking into account the specific dynamics of each actuator, require different levels of vehicle modeling, combined with automatic control approaches and optimal control techniques.

The article, which will focus solely on the basics of vehicle dynamics, will be in two parts.

The first part will describe the general equations of external vehicle dynamics. To this end, the first section will be devoted to the kinematics of undeformable wheels; the study of the tire in section 2 will allow us to introduce, in section 3, the specificities of this deformable element in the kinematics. Section 4 is devoted to the main results of aerodynamics applied to the automobile. Finally, in Section 5, the equations of dynamics will be written in all their generality, from which we'll derive the equations relating to the yaw-drift model and the roll model.

In the second part (forthcoming), the development of these two models will be discussed, together with an overview of "global chassis control". Sections 1 and 2 will focus on the yaw-drift model, studying stationary motion, stability and transient motion around stationary motion. In section 4, the rolling motion will be studied in a similar way to sections 1 and 2. Previously, in section 3, the anti-roll moment will be calculated from internal actions (springs, dampers, anti-roll...