THE TECTOLOGY OF DYNAMIC SYSTEMS AND THE PHENOMENON OF HYPERVALENCE INTERACTION IN THE STRUCTURAL EQUATIONS OF THE GENERALIZED ELECTRIC CIRCUIT

Abstract

The paper presents a number of the solutions of the important and interrelated theoretical problems, having technology-specific and general natural significance. Taken together and in the interaction with one another, they lay the  theoretical basis for the formation and development of the new trend in classical electrical engineering, characteristic feature of this trend is the construction of the generalized, regarding the number of the degrees of freedom, continuous in time, homogeneous or mixed by their nature dynamic systems,  as  of purely electrical and combined physical origin,  their structural analysis and formalization on the deductive basis of  the process of mathematical and physical identification.

In the connection of the above-mentioned the author determined and revealed the essence of the unknown general natural phenomenon of the hyperforce (hypervalence) interaction between the elementary structural links which is observed or can be observed in the dynamic systems with the concentrated parameters of the random physical nature and complexity in the process of their motion in the phase space under the impact of the internal and external forces. It is shown and mathematically proved that in general case the internal force interaction between the structural elements of the dynamic system is at the same time multidimensional and corresponds to the dimensionalities of the subspaces of the system topological space, which are determined by all the combinatorial combinations from the number n to the number k, where the number k belongs to the area 2 ≤ k ≤ n, and n is the number of the degrees freedom of this system. In such embedded  subspaces the available multidimensional forces of the random dimensionality are independent one from another. Among others, this simplifies the predominant, for grater part of theories and scientific systems, paradigm concerning the possibility of exceptionally  binary (k = 2) presentation of the character of the force interaction (and correspondingly mathematical relations) between the structural elements of the dynamic systems during their motion.

 Accounting  the phenomenon of the hyperforce (hypervalence) interaction considerably broadens  the classes of the studied dynamic systems.

On the example of the electric engineering systems the application of Lagrange-Maxwell equations enabled  to solve the number of decomposition problems, which form  the basis  of one of the fundamental problems of the theoretical electrical engineering – construction of the electric circuit. generalized by the number of the degrees of freedom .

The obtained results, namely topological structural diagram of the generalized electrical circuit and structurally determined system of differential equations of its motion (structural equations), today  have the highest degree of generalization and deductively embrace wide classes of the electrical circuits and systems – both already known and possible ones.