Modeling the Dynamics of BMW and Chevrolet

Abstract:
Nowadays, modern engineering relies more heavily on mathematical models and computer simulations than on experiments. The former is more efficient and accurate than the latter. Analyzing the mathematical model of the car is an effective way to find out the Motion trajectory when the car is moving. Python functions and Matlab are widely used to solve the dynamic problems of cars. This paper uses Python, single-variable calculus in mathematics, ordinary differential equations, Newton's 2nd Law of Motion, linear and angular momentum, equations of motion, and differentiation of functions. We put the trajectory x(t), y(t) and chi(t) the car vs time. According to the image, the movement state of the car at different conditions can be analyzed intuitively. Based on this, it will get the BMW non-linear and linear force model, BMW non-linear and linear lane change and show the plot of the front tire force and the front tire slip angle vs time. Besides, by adjusting the parameters of different car models, different operating results can be obtained so that the operating results of the car can be analyzed under different conditions.