Abstract:
In the article the mathematical model of the vehicle motion with elastic tires, which
describes the phases of the initial rectilinear motion on the longitudinal slope of the road is
shown. The mathematical model is valid for vehicle with two axles, one of which is driving
axel and provided that the stopped vehicle on a slope is kept from rolling only by braking the
non-driving axle. The aim of the study is to determine the equations to describe the process of
vehicle initial rectilinear motion during moving uphill, which take into account the tires
deformation energy on the stationary vehicle braking wheels. The presented equations
described in the article are reflect the dynamic state of the stationary vehicle on a slope and the
phase of its initial moving off uphill after brining the engine torque through the transmission to
the wheels of the drive axle. The system of equations describing the vehicle dynamic behavior
after brining torque to the drive wheels takes into account their false slip. The system of
equations is obtained from the general dynamic equation in the form of balance of the
elementary work of external forces and moments with the absence of external slipping of the
driving wheels. The mathematical model of the vehicle initial rectilinear motion on
a longitudinal slope of a highway described in the article can be used in theoretical basis for
analyzing and synthesizing control algorithms for automatic driver assistance systems during
vehicle initial motion.
