Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2021, Number 6, Pages 27–34 (Mi vmumm4436)  
Mechanics

The Mathieu equation near the boundaries of the second and third resonance zones

V. M. Budanova, L. F. Davudovab

a Lomonosov Moscow State University, Institute of Mechanics
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: A second order differential equation with periodic coefficients is considered. The reduction of this equation to a first order nonlinear equation is shown. The fourth approximation of the second resonance zone and the third approximation of the third resonance zone are constructed for the Mathieu's equation describing the behavior of solutions near the boundaries of these zones.
Key words: parametric resonance, equation with periodic coefficients.
Received: 02.10.2020
English version:
Moscow University Mechanics Bulletin, 2021, Volume 76, Issue 6, Pages 147–155
DOI: https://doi.org/10.3103/S0027133021060030
Bibliographic databases:
Document Type: Article
UDC: 531.36
Language: Russian
Citation: V. M. Budanov, L. F. Davudova, “The Mathieu equation near the boundaries of the second and third resonance zones”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 6, 27–34; Moscow University Mechanics Bulletin, 76:6 (2021), 147–155
Citation in format AMSBIB
\Bibitem{BudDav21}
\by V.~M.~Budanov, L.~F.~Davudova
\paper The Mathieu equation near the boundaries of the second and third resonance zones
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2021
\issue 6
\pages 27--34
\mathnet{http://mi.mathnet.ru/vmumm4436}
\zmath{https://zbmath.org/?q=an:1497.34045}
\transl
\jour Moscow University Mechanics Bulletin
\yr 2021
\vol 76
\issue 6
\pages 147--155
\crossref{https://doi.org/10.3103/S0027133021060030}
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