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Application of Lagrangian mechanics principles to electric circuit analysis

DOI 10.18127/j20700784–201810–10


Т.Ya. Shevgunov – Ph.D. (Eng.), Associate Professor, Moscow Aviation Institute (National Research University)
Е.N. Efimov – Ph.D. (Eng.), Research Scientist, Moscow Aviation Institute (National Research University)

In this paper, the application of Lagrangian mechanic principles is introduced for dynamic analysis of lumped-element electric circuits containing resistors and sources of independent voltages and currents. The proposed description of an electric circuit based on the generalized coordinates allows one to express the kinetic and potential energies for Lagrange’s function formulation. Using the practical examples of analysis of serial and parallel circuits, the methodical steps leading to direct Lagrangian and power function expressions and, then, obtaining the set of second-kind Euler–Lagrange equations are carried out. It was discussed that formal analogy between the generalized coordinates of masses in classical mechanics and charges in electric circuit theory allows making up a clear qualitative interpretation of the proposed analytical method that paves the way for its further application to analysis of complex physical systems.

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