Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1) design of new types of draft gears and air distributors; 2) development of methods for controlling the movement of conventional and connected trains; 3) creation of appropriate process flow diagrams; 4) development of energy-saving methods of train driving; 5) revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76); 6) when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7) when creating computer simulators for the training of locomotive drivers; 8) assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practical value. The practical value of the results obtained lies in the scientific validity and applied orientation of theoretical studies using mathematical models, the improvement of which will expand the range of problems to be solved, and increase the level of reliability of the results obtained. ботаны существующие математические модели для решения задач динамики поезда. Проведенный анализ научных статей, опубликованных в Украине, странах СНГ и за рубежом, позволяет определить наиболее актуальные области применения математических моделей. Практическая значимость. Практическое значение полученных результатов заключается в научной обоснованности и прикладной направленности теоретических исследований с использованием математических моделей, совершенствование которых позволит расширить круг решаемых задач, повысить уровень достоверности получаемых результатов.Ключевые слова: длинносоставные поезда; динамика поезда; математические модели продольных колебаний поезда; моделирование межвагонных соединений; научные статьи; продольные силы в поезде; тренажеры машинистов локомотивов ISSN 2307-3489 (Print), ІSSN 2307-6666 (Online) Наука та прогрес транспорту. Ві...
