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.
Highlights
Vehicle dynamics, including vehicle longitudinal motion, is a well-researched area and there are numerous very accurate mathematical models that describe various aspects of vehicle motion.Supported by a continuous increase in computing power, there is a distinctive trend towards more complex models that include more phenomena, resulting in high-fidelity models, which do not have closed-form solutions
We looked into the most common models from the area of vehicle dynamics in order to find out those that require only minor simplifications so that their solutions can be found in a closed form
We found model (1) as a prime example where relatively small simplifications allow the direct integration of the differential equations, leading to an interesting set of equations that describes vehicle longitudinal motion
Summary
Vehicle dynamics, including vehicle longitudinal motion, is a well-researched area and there are numerous very accurate mathematical models that describe various aspects of vehicle motion. In an attempt to calculate rolling resistance coefficient and vehicle aerodynamic coefficient, White and Korst [1] partially solved model (1) in a closed form while setting traction force and climbing resistance to zero. Such a solution is very different from the solution obtained in this paper. They note that simplifications allow the decoupling of the lateral, longitudinal, and vertical dynamics, and creation of models that describe each respective motion separately from the other two Such models allow partially analytical derivations of corresponding equations of motion, which, according to them, is useful for studying how input parameters influence the motion.
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