An Educational Model of the Movement of a Car on a Turn
Abstract
A mathematical model of the movement of a car in a turn is proposed. The movement of the car is described based on modeling the dry friction force acting on the wheels of the car, so that it takes into account the characteristic features associated with the rolling of the wheel and corresponds to the Coulomb-Amonton law when the wheels are locked. A mathematical model of car movement is derived from the laws of mechanics, representing a system of 6 1st-order differential equations, including a number of parameters characterizing
movement. The numerical solution of a system of equations can be obtained quite simply by students using standard procedures available in mathematical environments designed for mathematical modeling (MATLAB, Octave, etc.).The study of the model’s solutions is actually a computational experiment and allows, despite the simplicity of the model, to identify some qualitative features of the car’s movement that manifest themselves in practice.
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