 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 53, Issue 8 / 2018 | Next article >> |
| V.V. Sazonov and A.V. Troitskaya, "Periodic Solutions of Second-Order Differential Equations with Large Parameters," Mech. Solids. 53 (S2), 87-94 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
S2 |
Pages |
87-94 |
| DOI |
10.3103/S0025654418050151 |
| Title |
Periodic Solutions of Second-Order Differential Equations with Large Parameters |
| Author(s) |
V.V. Sazonov (Keldysh Institute of Applied Mathematics of RAS, Moscow, 125047 Russia, sazonov@keldysh.ru)
A.V. Troitskaya (Moscow State University, Moscow, 119991 Russia, an.troitskaya@gmail.com) |
| Abstract |
A second-order differential equation containing a large parameter is considered. Such an
equation can be interpreted as an equation of constrained oscillations of a mechanical system with one
degree of freedom, provided that the fundamental frequency of the system substantially exceeds the
external frequency. We provide a new proof of the existence of a periodic solution of that equation such
that it is close to the periodic solution of the corresponding degenerate equation. That proof is
obtained by means of the Poincaré method. |
| Keywords |
second-order differential equations, large parameter, periodic solutions, Poincaré method, Lichtenstein method |
| Received |
20 March 2018 |
| Link to Fulltext |
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