Objective: to describe the speed of the car at each section of the descent part of the hump using the principles of classical mechanics; to get a generalized model of the speed of movement of the car at the estimated point of the hump, which allows speeding up the process of building graphs and changing the kinematic characteristics of the car’s movement; to present the change in the instantaneous speed of movement of the car along the entire length of the descent part of the hump in the form of a graph of the step function. Research methods: the paper applies mainly theoretical research methods: analysis and modeling. The paper widely uses the methods of classical mechanics. Main results: Based on the application of a single impulse, a mathematical model has been developed for the movement of a car along the entire length of the descent part of the hump. The description of the dynamics of the car rolling from the hump, including sections of brake positions, in a generalized form was made for the first time. Conclusions and their significance for the industry: The change in the instantaneous speed of movement along the entire length of the descent part of the hump is presented in the form of a step function graph for the first time. The proposed model of a generalized mathematical notation of an instantaneous change in the speed of a car rolling down the descent part of the hump has a practical significance. This model allows calculating instantaneous values of the speeds of movement of the car from the top of the hump to the design point in a continuous mode, which makes it possible to accelerate the process of building graphs of changes in accelerations, speeds, and time of car’s movement. The resulting model allows quickly analyzing the mode of shunting cars from the humps, the combination of power of brake positions and improve the accuracy of determining the permissible velocity of impact of cars in the sorting yards. This paper is the most important step for solving a promising task of designing an automated system for calculating the dynamic characteristics of a car in a hump yard.

railway, station, marshalling hump, wagon, Heaviside discontinuous functions, a generalized mathematical notation of the instantaneous speed of a carriage along a slide profile