## A completion of A. Bressan’s work on axiomatic foundations of the Mach-Painlevé type for various classical theories of continuous media. I: Completion of Bressan’s work based on the notion of gravitational equivalence of affine inertial frames.(English)Zbl 0774.73004

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)], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevé point of view, is completed here in two alternative ways; in that work, among other things, affine inertial frames are defined within classical kinematics.
Here, in part I, a thermodynamic theory of continuous bodies, in which electrostatic phenomena are not excluded, is dealt with. The notion of gravitational equivalence among affine inertial frames and the notion of gravitational isotropy of these frames are introduced; it is shown that the isotropic inertial frames, gravitationally equivalent to a fixed frame of this kind, are those linked to this by a (possibly improper) Galilean transformation. The Euclidean physical metric on inertial spaces is consequently determined, without introducing it as a primitive notion; and this is the main completion of $$(*)$$ which is obtained here.

### MSC:

 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids 74A15 Thermodynamics in solid mechanics 70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics

Zbl 0774.73003