Closed-Form Solution of a Special Case of a Vehicle Longitudinal Motion Model

Abstract

One of the most common approaches in modern engineering research, including vehicle dynamics, is to formulate an accurate, but typically complex, mathematical model of a system or phenomenon and then use a software package to solve it. Typically, the solution is obtained in the form of a large data set, which may be difficult to analyse and interpret. This paper represents a purely theoretical analysis of a special case of vehicle longitudinal motion. Starting from a simplified mathematical model, a set of transcendental equations was derived that represents the exact solution of the model (i.e., in a closed form). The equations are analysed and interpreted in terms of what is their physical meaning. Although the equations derived here have only limited application in studying real world problems, due to the simplicity of the mathematical model, they offer a deeper insight into the nature of vehicle longitudinal motion.

Design of an Aftermarket Hybridization Kit: Reducing Costs and Emissions Considering a Local Driving Cycle

“…In the literature, models of vehicle longitudinal dynamics and vehicle components are often implemented in MATLAB TM [37,[39][40][41]. All the equations presented here have been implemented by the authors by means of MATLAB/Simulink TM block diagrams.…”