This work touches upon the tasks of describing regional socio-economic development. The nature of the considered problem indicates the fact that the only relevant tool here is mathematical modeling. In this paper, the application of mathematical modeling is considered for the problem of managing regional development. The results of calculations based on the regional dynamic model that passes through the hierarchy of instabilities (the correspondence of the same stationary points of the model to different parameters) are presented. These instabilities lead to increasingly complex structures.

This paper considers a modern approach of K&C parameters stability analysis using the suspension MBS model of a short-wheelbase electric vehicle. According to the results of the work, even minor errors in suspension hardpoints positioning when overlaying can greatly affect the K&C parameters of car suspensions. Using MBS models, quasi-static K&C events have been simulated. In the same way the dependences of the suspension K&C parameters are numerically determined. Moreover, these calculations were made with different hardpoints positions for joints of wishbones fastening on a frame, and joint of a steering rod with a steering rack. The influence of suspension hardpoints displacement on the K&C parameters of the vehicle was estimated. As a result, recommendations are made for production positioning tolerances of suspension hardpoints in order to avoid deterioration of K&C parameters. Basically, the appearance of inaccuracies in the positioning of hardpoints leads to critical changes in anti-dive, anti-lift, kingpin inclination angle, bump camber and bump steer parameters.

The paper considers the scientific and technical essence of forming and developing computer engineering from the very beginning of engineering analysis and design to the latest achievements in this field. In the course of their work, the authors, following the traditions of St. Petersburg Polytechnic University, rely on the development of the fundamental foundations of the natural science knowledge, which has always served as a measure of engineering development. We consider a fairly long historical period from the time of I. Newton, L. Euler and J.-L. Lagrange, who laid the foundation of engineering sciences, through the XIX and XX centuries to our time. The authors focus on the most important tools of research, for both natural phenomena and engineering calculations, - tools of mathematical analysis. Nearly in the second half of the XX century, with the advent of computers, this tool acquired the features of mathematical modeling technologies. Today this mathematical modeling is the basis for development of advanced methods of computer engineering. But this very tool is evolving at an extremely rapid pace, integrating the most advanced approaches of mathematics, physical mechanics, computer (supercomputer) technologies and information and communication resources. This development, together with a number of other computer technologies, radically changed the concept of the traditional, centuries-old production process and gave rise to the idea of the Digital industry.

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The article considers the problem of optimal design of car body elements (longitudinal members) according to the chosen criteria. Both the questions of formulation of the optimization task and individual problems of its solution are studied. The mathematical statement of the problem is considered. Thus, the most attention is given to consideration of realisation of used numerical procedure of optimization. The system of numerical calculations is based on the most widely spread software systems for engineering analysis and design. The developed scripts on Python programming language are briefly considered. Results of optimization of longitudinal members of the car are given.