Towards axiomatic foundations of the Mach-Painlevé type for classical or relativistic theories of continuous media.

*(English)*Zbl 0774.73003The axiomatic foundations of classical mechanics stated in an earlier paper by the author [Rend. Sem. Mat. Univ. Padova 32, 55-230 (1962; Zbl 0114.148)] and those of kinematics for classical physics or special relativity presented in a paper by the author and A. Montanaro [ibid. 68, 163-182 (1982; Zbl 0538.70001)] refer to particle systems from the Mach-Painlevé point of view. The main aim of this work is what in our opinion is the main step of the extension of previous works to continuous media. Furthermore, we aim at showing that also well-developed classical theories of continuous media can be based on the present work; therefore some structural properties of continuous bodies are treated as examples, and inertial mass is defined. The completion of the present extension of the author [op. cit.] has already been performed by A. Montanaro [see the following entries].