Modeling of Mechanical and Electrical Systems with Fractal Structure Under Impulse Action and Coherent Acceleration

This study explores the applications of extended Gauss–Hertz variational principles to determine the evolution of complex systems under the influence of impulse actions, coherent accelerations, and their application to electrophysical systems with fractal elements. Impulsive effects on systems initiate coherent accelerations (including higher-order accelerations, such as modes with intensification), leading to variations in connections, structure, symmetry, and inertia; the emergence of coherence; and the evolution of fractal elements in electrophysical circuits. The combination of results from the non-local Vlasov theory and modifications to the Gauss–Hertz principle allows for the formulation of a variational principle for the evolution of fractal systems. A key feature of this variational principle is the ability to simultaneously derive equations for both the system’s dynamics and the self-harmonizing evolution of its internal symmetry and structure (e.g., fractal parameters).