Abstract
The article presents the application of general stability theory to the study of road traffic stability immediately after an impact (crash, collision). It turns out that when modelling a collision, vehicles can be treated as colliding masses and dynamical systems can be assigned to this phenomenon.
Highlights
Stability theory deals with the qualitative analysis of dynamic systems and can be used to study the motion stability
The point is that after hitting a vehicle or other obstacle, the vehicles involved in this event remain on the same lane, i.e. they do not block the adjacent lane, which reduces the likelihood of another accident (Figure 1)
Dynamical systems can have many attractors and it depends on the initial condition of a given orbit towards which attractor the system will converge [1]
Summary
Stability theory deals with the qualitative analysis of dynamic systems and can be used to study the motion stability. In the case of n=2, the stability of trajectory indicates that in the phase space each trajectory starting in tt0 from the circle of the radius δ will not leave the circle of the radius εε in any arbitrary time tt > tt0 If this is not satisfied, the system is not stable, which is not advantageous from the practical point of view. The process of vehicles colliding is an interaction between them, in which the impact time is very brief leading to a rapid change in their velocity and resulting in the creation of very large impact forces acting on vehicles [3] It is the value that reflects he character of the impact and from the perspective of vehicle crash, it can be assumed that it is a number in the range (0, 1) because the collision is accompanied by losses of the kinetic energy of the vehicles
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