 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| Yu. A. Chirkunov, "Group foliation of the Lamé equations of the classical dynamical theory of elasticity," Mech. Solids. 44 (3), 372-379 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
3 |
Pages |
372-379 |
| DOI |
10.3103/S0025654409030066 |
| Title |
Group foliation of the Lamé equations of the classical dynamical theory of elasticity |
| Author(s) |
Yu. A. Chirkunov (Novosibirsk State University of Economics and Management, Kamenskaya 56, Novosibirsk, 630070 Russia, chr01@rambler.ru) |
| Abstract |
We perform the group foliation of the system of Lamé equations of the classical dynamical theory of elasticity for an infinite subgroup contained in a normal divisor of the main group. The resolving system of this foliation includes the following two classical systems of mathematical physics: the system of equations of vortex-free acoustics and the system of Maxwell equations, which allows one to use wider groups to obtain exact solutions of the Lamé equations. We obtain a first-order conformal-invariant system, which describes shear waves in a three-dimensional elastic medium. We also give examples of partially invariant solutions. |
| References |
| 1. | V.Yu. Prudnikov and Yu.A. Chirkunov,
"Group reduction of the Lamé Equations,"
Prikl. Mat. Mekh. 52 (3), 471-477 (1988)
[J. Appl. Math. Mech. (Engl. Transl.) 52 (3), 366-371 (1988)]. |
| 2. | L.V. Ovsyannikov,
Group Analysis of Differential Equations
(Nauka, Moscow, 1978; Academic Press, New York, 1982). |
| 3. | F. Frank and R. Mises (Editors),
Differential and Integral Equations of Mathematical Physics
(ONTI, Leningrad-Moscow, 1937) [in Russian]. |
| 4. | N.H. Ibragimov,
Transformation Groups Applied To Mathematical Physics
(Nauka, Moscow, 1983; Springer, New York, 1985). |
| 5. | A.F. Sidorov, V.P. Shapeev, and N.N. Yanenko,
The Method of Differential Constraints and Its Applications in Gas Dynamics
(Nauka, Novosibirsk, 1984) [in Russian]. |
| 6. | V.B. Poruchikov,
Methods of Dynamical Elasticity
(Nauka, Moscow, 1986) [in Russian]. |
|
| Received |
25 June 2008 |
| Link to Fulltext |
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