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The work presents different ways of modeling transport issues, with particular consideration of contact problems. Special computational approaches and the use of analogy in the field of electrical engineering strengthened the efficiency of developed methods of modeling. It has been shown that such computational tools, as monic power polynomials power modified numerical triangles, the power functional used in the calculation of the electrical networks and circuits may be used to study the of contact problems with the rail and wheels.The study also showed that the calculation of energy transfer using the concept of one-period energy can be adapted to describe the energetic processes of contact wheel - rail.Modeling of the impact of transport on the environment is based on the concept of the study of the 2-D system with the use of an elastic half-space as a model of soil. The results presented of this work are part of the research on modeling the dynamics of rail vehicle conducted by a number of specialist research centers in the world in order to maintain high standards of ride comfort and ensure transport safety while respecting the principles of environmental protection.
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