PHYSICAL INTERPRETATION OF PARAMETRIC RESONANCE BY ENERGY APPROACH

Authors

  • LERNIK PETROSYAN ASPU
  • GAREGIN ELOYAN ASPU

DOI:

https://doi.org/10.24234/scientific.v1i46.132

Keywords:

Oscillatory contour , parametric resonance, reactance’s, contour energy, capacitance, inductance, step change

Abstract

The object of study is the phenomenon of parametric resonance from the point of view of physical interpretation.

             The purpose of the study is to identify one of the special cases of the phenomenon of parametric resonance associated with an oscillating reference frame, when the parametric system contains time-dependent capacitive and inductive reactance.

Based on physical measurements using a simple mathematical apparatus, qualitative analyzes are given that combine the harmony of mathematical and physical approaches.

Parametric resonance is an extremely complex phenomenon associated with the imbalance of linear systems. Therefore, disequilibrium occurs due to small accumulations in an infinite time interval. Like small clusters, infinite time intervals are not suitable for graphical representation and physical interpretation of resonance. For this reason, the study of parametric resonance leads to formal mathematical problems that are idealized and difficulties arise when comparing them with practical ones.

Theoretical methods, analyzing professional literature, also a quantitative analysis of the obtained results are used.

In the radio-physical literature, insufficient attention is paid to the study of two non-stationary reactivity, although the possibilities of using a parametric circuit can be significantly expanded. The article analyzes this problem, since it was solved exclusively by physical methods.

References

Akademik L. I. Mandel'shtam. (1972). Lekcii po teorii kolebanij (Lectures on the theory of oscillations). Moskva, Nauka.

Biryuk N. D., Krivcov A. YU., YUrgelas V. V. (2013). Analiz ustojchivosti parametricheskogo kontura, osnovannyj na pervom metode Lyapunova (Stability analysis of a parametric contour based on the first Lyapunov method). Vestnik VGU. Seriya Fizika. Matematika, 1, 13–20.

Demidovich B. P. (1967). Lekcii po matematicheskoj teorii ustojchivosti (Lectures on the mathematical theory of stability). Moskva, Nauka.

Zajcev V. F., Polyanin A. D. (1997). Spravochnik po linejnym obyknovennym differencial'nym uravneniyam (Handbook of Linear Ordinary Differential Equations). Moskva, Faktorial.

Mandel'shtam L.I. (1947). O Vozbuzhdenii kolebanij v elektricheskoj kolebatel'noj sisteme pri pomoshchi periodicheskogo izmeneniya emkosti (On Excitation of oscillations in an electrical oscillatory system by means of periodic changes in capacitance). (2nd ed.). Izd. AN SSSR.

YAkubovich V. A., Starzhinskij V. M. (1972). Linejnye differencial'nye uravneniya s periodicheskimi koefficientami i ih prilozheniya (Linear differential equations with periodic coefficients and their applications). Moskva, Nauka.

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Published

2023-04-28