Spectral analytical methods of research of several classes of
non-autonomous model systems
A. A.
Egorov
1,
Yu. A. Konyaev
2,
Nguyen Viet Khoa 3
1
A.M. Prokhorov General Physics Institute of the Russian
Academy of Sciences
2
National Research University “Moscow Power Engineering
Institute”
3
Kien
Giang Teacher Training College,
Vietnam
The paper is received on January
18, after correction - on February 17, 2016
Abstract. The presented work is devoted to the development of known mathematical
methods, and also working out of new spectral analytical methods and
constructive algorithms necessary at the analysis of various theoretical linear
and quasi-linear dynamic models, realized in the form of systems of ordinary
differential equations with periodic, polynomial and polynomially periodic
matrix. Such models are of great importance at studying of some real physical
phenomena and processes. The basic attention in work is given to consideration
of a spectral variant of the averaging method at the analysis of non-autonomous
systems of differential equations with the periodic matrix, describing
regularly perturbed systems. Some results of use of the specified methods for
research of the specific real physical phenomena representing doubtless
practical interest also are resulted in the paper. In particular the interaction of two
coupled linear oscillator in the absence of resonance phenomena is analyzed.
Key words: non-autonomous systems, Mathieu equation, parametric resonance, spectral
method, differential equations with periodic matrix, study of stability, linear
oscillator.