Summary
An axiomatic approach to the study of relative continuum mechanics in curved space-time is proposed. The explicit assumptions are: a) existence of the energy-momentum tensor Tij, satisfying the equations of motion Tij ‖j=0, and b) existence of the congruence of stream-lines of the given continuum. The argument relies on a relativistic extension of the Lagrangian viewpoint, and involves the analysis of the relative dynamical behaviour of an arbitrary infinitestimal globule Δ of continuum in a given frame of reference [Γ]. The plan is fulfilled in two steps:1) geometrical theory of the Lagrangian viewpoint, valid for any type of continua satisfying the stated requirements;2) physical applications, illustrating the general theory in the case of an energy-momentum tensor of the form Tij=μ 0 ViVj—Sij.
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E. Massa,Relative continuum mechanics in general relativity. — I:Kinematical foundations, Annali di Matematica,117 (1978), p. 311.
G. E. Mase,Continuum Mechanics, Schaum's Outline Series, McGraw Hill, New York, 1970.
L. Landau -E. Lifchitz,Mécanique des Fluids, Editions Mir, Moscow (1971).
E. Massa, Gen. Rel. Grav.,5 (1974), p. 555.
E. Massa, Gen. Rel. Grav.,5 (1974), p. 573.
C. Cattaneo, Nuovo Cimento,10 (1958), p. 318.
C. Cattaneo, Nuovo Cimento,11 (1959), p. 733.
C. Cattaneo, Nuovo Cimento,13 (1959), p. 237.
J. L. Synge,Relativity: the General Theory, North Holland, Amsterdam, 1960.
J. L. Synge,The Relativistic Gas, North Holland, Amsterdam, 1957.
C. Møller,The Theory of Relativity, Clarendon Press, Oxford, 1952.
H. Goldstein,Classical Mechanics, Addison-Wesley, Reading (Massachusetts) and London, 1959.
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Entrata in Redazione il 22 novembre 1977.
Lavoro eseguito nell'ambito dell'attività del Gruppo Nazionale per la Fisica Matematica del C.N.R.
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Massa, E. Relative continuum mechanics in general relativity. Annali di Matematica 121, 59–76 (1979). https://doi.org/10.1007/BF02411993
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DOI: https://doi.org/10.1007/BF02411993