# Vehicle Planar Dynamics

• Reza N. Jazar
Chapter

## Abstract

In this chapter we study the planar model of vehicles to examine maneuvering by steering as well as the wheel torque control. The wheel torque and steer angle are the inputs and the longitudinal velocity, lateral velocity, and yaw rate are the main output variables of the planar vehicle dynamics model. The planar vehicle dynamic model is the simplest applied modeling in which we assume the vehicle remains parallel to the ground and has no roll, no pitch, and no bounce motions. The planar motion of vehicles has three degrees of freedom: translation in the x and y directions, and a rotation about the z-axis. The longitudinal velocity vx along the x-axis, the lateral velocity vy along the y-axis, and the yaw rate $$r=\dot {\psi }$$ about the z-axis are the outputs of the dynamic equations of motion.

By ignoring the roll motion as well as the lateral load transfer between left and right wheels, we define a simplified two-wheel model for the vehicle.

The four-wheel planar vehicle model is an extension to the two-wheel planar vehicle model to include the lateral weight transfer. The four-wheel planar model provides us with better simulation of drifting vehicles. This model is capable to simulate drift of vehicles as well as simulation of different tire-wheel interaction for all four tires of a vehicle.

## Keywords

Tire force system Vehicle dynamics Vehicle kinematics Bicycle model Four-wheel vehicle model Steady-state dynamics Drift model

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