# MODELING OF THE MECHANISM OF VEHICLE OVERTURNING IN THE PROCESS OF DEVELOPMENT OF ROAD TRAFFIC ACCIDENT

Keywords: road traffic accident, vehicle, lateral obstacle, overturning, modeling.

### Abstract

The development of mathematical models of vehicle overturning has been given significant attention by many researchers because of the need to obtain reliable information on the circumstances of road traffic accidents. Research of road traffic accidents with the overturning of vehicles is related with the difficulty to determinate the mechanism of overturning, because expert calculation methods do not always use the adapted mathematical models. Most of the methods focus on determining the minimum (critical) speed of vehicles, which leads to its overturning. However, the real speed of vehicles before overturning can be much higher. In this paper, a mathematical model of the process of vehicle overturning after a collision with an immovable lateral obstacle is given. Thus the overturning moment caused by the inertia forces acts on the vehicle, and the moment from the gravity that holds the vehicle from overturning. It is necessary to mark that the shoulder of moment from gravity changes from a maximal value to 0 in the process of vehicle overturning. The mathematical model is based on the basic equation of dynamics for rotational motion. The developed mathematical model is a nonlinear homogeneous differential equation of second order. A solution of this equation is obtained that allows us to determine the conditions for the vehicles overturning and to investigate the basic parameters of the movement of vehicles in the process of overturning from the moment when the center of mass of the vehicle begins to rise until the moment of its maximum lifting. A comparison of the results of calculating the critical speed of vehicles with results obtained on the basis of the law of energy conservation was carried out. The results are fully agreed. The numerical results obtained using a mathematical model for a particular vehicle have been analyzed.

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