On the variational method of derivation of equations of state for a material medium and a gravitational field. (English. Russian original) Zbl 0441.76101
J. Appl. Math. Mech. 42, 827-838 (1979); translation from Prikl. Mat. Mekh. 42, 771-780 (1978).
MSC:
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 49S05 | Variational principles of physics |
| 83C99 | General relativity |
| 85A40 | Astrophysical cosmology |
References:
| [1] | Sedov, L. I., On the energy-momentum tensor and macroscopic internal interactions in a gravitational field and in material media, Dokl. Akad. Nauk SSSR, Vol. 164, No. 3 (1965) |
| [2] | Sedov, L. I., Mathematical methods of constructing new models of continuous media, Uspekhi Matem. Nauk, vol. 20, No. 5 (1965) · Zbl 0151.37003 |
| [3] | Sedov, L. I., (Mechanics of the Continuous Medium, Vol. 1 (1976), Nauka: Nauka Moscow) · Zbl 0185.54002 |
| [4] | Sev, L. I., On conditions at second-order discontinuities in the theory of gravitation, PMM, Vol. 36, No. 1 (1972) |
| [5] | Sedov, L. I., On the local equation of energy in a gravitational field, Dokl. Akad. Nauk SSSR, Vol. 240, No. 3 (1978) · Zbl 0419.53019 |
| [6] | Zhelnorovich, V. A., Models of media with internal electromagnetic and mechanical moments, (Collection: Problems of Hydrodynamics and Mechanics of the Continuous Medium (1969), Nauka: Nauka Moscow) · Zbl 0197.23701 |
| [7] | Logunov, A. A.; Folomeshkin, V. N., The problem of energy-momentum and the theory of gravitation, Teoret.i Matem. Fizika, Vol. 32, No. 3 (1977) · Zbl 0362.53020 |
| [8] | Mindlin, R. D., Second gradient of strain and surface tension in linear elasticity, Int. J. Solid Structures, Vol. 1, No. 4 (1965) |
| [9] | Zhelnorovich, V. A., Variattonal principle and equations of state for continuous media, Dokl. Akad. Nauk SSSR, Vol. 184, No. 1 (1969) · Zbl 0202.24703 |
| [10] | Zhelnorovich, V. A., On integral laws of conservation for continuous media in the general theory of relativity, Dokl. Akad. Nauk SSSR, Vol. 186, No. 1 (1969) · Zbl 0202.24703 |
| [11] | Zhelnorovich, V. A., On the problem of determining energy-momentum in the general theory of relativity, Dokl. Akad. Nauk SSSR, Vol. 201, No.5 (1971) |
| [12] | Lur’e, M. V., Use of the variational principle for the study of propagation of surfaces of discontinuity in a continuous medium, PMM, Vol. 33, No. 4 (1969) · Zbl 0214.52301 |
| [13] | Lorentz, H. A., Over Einstein’s Theorie der Zwaartekracht, Amst. Akad. Versl., Vol. 25 (1916) · JFM 46.1329.02 |
| [14] | Einstein, A., Hamiltonsche Prinzip und allgemeine Relativitätstheorie, Sitzb. Kgl. preuss. Akad., Berlin, Vol. 2 (1916) · JFM 46.1294.01 |
| [15] | Shawten, I.; Stroik, D. J., Introduction to New Methods of Differential Geometry (1948), Izd. Inostr. Lit: Izd. Inostr. Lit Moscow |
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