 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| V. V. Vasil'ev and L. V. Fedorov, "An elasticity problem for a gravitating ball and some geometrical effects," Mech. Solids. 38 (1), 67-74 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
1 |
Pages |
67-74 |
| Title |
An elasticity problem for a gravitating ball and some geometrical effects |
| Author(s) |
V. V. Vasil'ev (Moscow)
L. V. Fedorov (Moscow) |
| Abstract |
We consider a homogeneous isotropic elastic ball loaded by volume forces
determined by Newton's theory of gravitation. The stress state of the ball
determined by the solution of the elasticity problem is utilized
to specify the energy-momentum tensor in the linearized problem of general
relativity, and the geometrical properties of the resulting
Riemannian space are analyzed. The results obtained here are compared with
the linearized solutions of general relativity problems for a stress-free
and a liquid ball, and represent a generalization of these solutions to the
case of an elastic ball. We formulate the general problem of general
relativity for an elastic medium. |
| References |
| 1. | Ya. B. Zel'dovich, S. I. Blinnikov, and N. I. Shakura,
Physical Principles of Star Structure and Evolution [in Russian], Izd-vo
MGU, Moscow, 1981. |
| 2. | V. Z. Vlasov, "Equations of strain
continuity in curvilinear coordinates," in Selected Works. Volume 1 [in
Russian], Izd-vo AN SSSR, Moscow, 1962. |
| 3. | J. L. Synge, Relativity: the General Theory [Russian translation], Izd-vo Inostr.
Lit-ry, Moscow, 1963. |
| 4. | N. A. Kil'chevskii,
Fundamentals of Tensor Calculus and its Applications in Mechanics [in Russian],
Naukova Dumka, Kiev, 1972. |
| 5. | E. Schmutzer, Theory of Relativity. Modern View [Russian
translation from German], Mir, Moscow, 1981. |
| 6. | V. V. Vasil'ev and l. V. Fedorov,
"On an elasticity problem posed in stresses,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 82-92, 1996. |
| 7. | L. D. Landau and E. M. Lifshitz,
Theoretical Physics. Volume 2. Field Theory [in Russian], Nauka, Moscow, 1988. |
| 8. | V. V. Vasil'ev,
"Stress state of solids and some geometrical effects,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 30-34, 1989. |
| 9. | C. W. Misner, K. S. Thorne, and J. A. Wheeler,
Gravitation. Volume 2 [Russian translation], Ainshtain, Bishkek, 1996. |
| 10. | A. M. Prokhorov (Editor), Encyclopaedia of Physics [in Russian], Izd-vo
Sov. Entsiklopediya, Moscow, 1988. |
| 11. | P. K. Rashevskii,
Riemannian Geometry and Tensor Analysis [in Russian], Nauka, Moscow, 1976. |
|
| Received |
26 December 2001 |
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