Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2017, Number 1, Pages 42–47 (Mi vmumm43)  
This article is cited in 2 scientific papers (total in 2 papers)

Mechanics

A form of the solution to the Mathieu equation

V. M. Budanov

Lomonosov Moscow State University, Institute of Mechanics
Full-text PDF (653 kB) Citations (2)
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Abstract: A linear transformation of a special type is introduced to express the general solution to a second-order differential equation with a periodic coefficient using a particular solution to an auxiliary second-order nonlinear system with a periodically perturbed right-hand side. It is numerically shown that there exist periodic solutions to the auxiliary system outside the instability zones of the Mathieu equation. The obtained estimates for the instability zones are in agreement with known results.
Key words: system with periodic coefficients, nonlinear system, Mathieu equation.
Received: 21.09.2015
English version:
Moscow University Mechanics Bulletin, 2017, Volume 72, Issue 1, Pages 7–12
DOI: https://doi.org/10.3103/S0027133017010022
Bibliographic databases:
Document Type: Article
UDC: 531.36
Language: Russian
Citation: V. M. Budanov, “A form of the solution to the Mathieu equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 1, 42–47; Moscow University Mechanics Bulletin, 72:1 (2017), 7–12
Citation in format AMSBIB
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\paper A form of the solution to the Mathieu equation
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\issue 1
\pages 7--12
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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