The work of axiomatization of various classical theories on continuous bodies from the Mach-Painleve point of view [Bressan, same journal Cl. Sci. Fis. Mat. Natur. (8) ´ 19 (1987), no. 1, 1–21; MR1006945 (90g:73013)] is completed here in a way which—unlike our Part I [ibid. Cl. Sci. Fis. Mat Natur. (8) 81 (1987), no. 1, 35–46; see the preceding review]—is suitable for extension to special relativity. The main reason for this is the fact that gravitation can be excluded in all the theories on continuous bodies considered here. Following Bressan [Rend. Sem. Mat. Univ. Padova 32 (1962), 55–213], the notion of (physical) equivalence among affine inertial frames, and that of (physical) isotropy of these frames are introduced; it is shown that the isotropic inertial frames equivalent to a fixed frame of this kind are those linked to this frame by a (proper) Galilean transformation. As in Part I, the Euclidean physical metric on inertial spaces is consequently determined, without introducing it as a primitive notion. The treatment of Part II refers to thermodynamic theories for continuous bodies and, as a particular case, to purely mechanical theories. In this last case, the primitive concepts are only the purely kinematical ones, presented by Bressan [op. cit., 1987].

A completion of A. Bressan's work on axiomatic foundations of the Mach Painleve` type for various classical theories of continuous media. Part 2: Alternative Completion of Bressan's work, fit for extension to special relativity

MONTANARO, ADRIANO
1987

Abstract

The work of axiomatization of various classical theories on continuous bodies from the Mach-Painleve point of view [Bressan, same journal Cl. Sci. Fis. Mat. Natur. (8) ´ 19 (1987), no. 1, 1–21; MR1006945 (90g:73013)] is completed here in a way which—unlike our Part I [ibid. Cl. Sci. Fis. Mat Natur. (8) 81 (1987), no. 1, 35–46; see the preceding review]—is suitable for extension to special relativity. The main reason for this is the fact that gravitation can be excluded in all the theories on continuous bodies considered here. Following Bressan [Rend. Sem. Mat. Univ. Padova 32 (1962), 55–213], the notion of (physical) equivalence among affine inertial frames, and that of (physical) isotropy of these frames are introduced; it is shown that the isotropic inertial frames equivalent to a fixed frame of this kind are those linked to this frame by a (proper) Galilean transformation. As in Part I, the Euclidean physical metric on inertial spaces is consequently determined, without introducing it as a primitive notion. The treatment of Part II refers to thermodynamic theories for continuous bodies and, as a particular case, to purely mechanical theories. In this last case, the primitive concepts are only the purely kinematical ones, presented by Bressan [op. cit., 1987].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/134776
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