A completion of A. Bressan’s work on axiomatic foundations of the Mach-Painlevé type for various classical theories of continuous media. II: Alternative completion of Bressan’s work, fit for extension to special relativity. (English) Zbl 0774.73005

Summary: The work [(*) A. Bressan, Atti Accad. Naz. Lincei, Mem., Cl. Sci. Fis. Mat. Nat., VIII. Ser., Sez. I 19, No. 1, 1–21 (1987; Zbl 0774.73003)] of axiomatization of various classical theories on continuous bodies from the Mach-Painlevé point of view, is completed here in a way which – unlike Part I [see the preceding entry Zbl 0774.73004] – is suitable for extension to special relativity. The main reason of this is the fact that gravitation can be excluded in all the theories on continuous bodies considered here. Following Bressan’s earlier work [A. Bressan, Rend. Sem. Mat. Univ. Padova 32, 55–230 (1962; Zbl 0114.14902)], 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 is referred to thermodynamic theories for continuous bodies and, as a particular case, to purely mechanic theories. In this last case, the primitive concepts are only the purely kinematical ones, presented in \((*)\).


74Axx Generalities, axiomatics, foundations of continuum mechanics of solids
74A15 Thermodynamics in solid mechanics
83A05 Special relativity