МОДЕЛЮВАННЯ ПРОЦЕСІВ НАКОПИЧУВАННЯ ЕНЕРГІЇ В ЕЛЕКТРОМЕХАНІЧНИХ СИСТЕМАХ НА ПІДСТАВІ ПОЛОЖЕНЬ ТЕОРЕМИ ВІРІАЛУ

Abstract

Purpose. According to the results of research initiated by revealing the paradox of energies of disturbed lever equilibrium, and on the basis of the virial theorem, a formalized physical mechanism of accumulation of viral energy of forces acting in the system of material points is established. The equilibrium state is introduced into the mathematical apparatus of the viral theorem as an initial condition for averaging energy over time, which complements the statistical method with an agreed formalized physical mechanism of energy accumulation due to the imbalance of the system. Instead, the method of statistical averaging of energy over time remains unchanged, and from a tool for quantitative assessment of stored energy is transformed into a universal tool for modeling energy storage processes. The results are verified by comparing the correspondence of the viral theorem of the formalized physical mechanism of energy accumulation and the formalized physical mechanism of energy conversion. Methodology. Within the mathematical apparatus of the viral theorem, formalized physical mechanisms of energy accumulation and conversion create opportunities to combine a wide range of existing methods of mathematical modeling and energy averaging over time, for example, with probabilistic analysis of stochastic discrete-continuous systems and processes to develop new methods and means of modeling energy and analysis of the behavior of physical systems of different nature. Results. Theoretical results of modeling and analysis of energy storage processes of electrostatic and magnetic fields allow to eliminate contradictions in the understanding of the physical content of the factor ½ in the energy formulas of the capacitor and inductor and explain it in accordance with the viral theorem. Originality. For the first time, the state of equilibrium of a system is considered as an initial condition for averaging energy over time, which complements the statistical method of the mathematical apparatus of the viral theorem with an agreed formalized physical mechanism of energy accumulation due to system imbalance. Instead, the method of statistical averaging of energy over time remains unchanged and from a tool for quantitative assessment of stored energy is becoming a universal tool for modeling the course of energy storage processes. On the basis of the formalized physical mechanism of energy accumulation the methodical bases of development of mathematical models of dynamics of processes of energy accumulation which provide a combination with a wide range of the developed methods of mathematical modeling, in particular, means of modeling energy storage and analysis of the behavior of physical systems of different nature. Practical value. Of practical importance is a method developed on the basis of simulation results of converting current energy into pulse energy, which combines the properties of disturbed energy balance and duality of capacitor and inductor, and consists in controlling the simultaneous accumulation and conversion of energy pulse repetition. Figures 6, references 14.