A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames

Adriano Montanaro

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1987)

  • Volume: 81, Issue: 1, page 35-46
  • ISSN: 0392-7881

Abstract

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The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè 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 [3] which is obtained here.

How to cite

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Montanaro, Adriano. "A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 81.1 (1987): 35-46. <http://eudml.org/doc/289244>.

@article{Montanaro1987,
abstract = {The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè 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 [3] which is obtained here.},
author = {Montanaro, Adriano},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Axiomatization; Continuum; Thermodynamics},
language = {eng},
month = {3},
number = {1},
pages = {35-46},
publisher = {Accademia Nazionale dei Lincei},
title = {A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames},
url = {http://eudml.org/doc/289244},
volume = {81},
year = {1987},
}

TY - JOUR
AU - Montanaro, Adriano
TI - A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1987/3//
PB - Accademia Nazionale dei Lincei
VL - 81
IS - 1
SP - 35
EP - 46
AB - The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè 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 [3] which is obtained here.
LA - eng
KW - Axiomatization; Continuum; Thermodynamics
UR - http://eudml.org/doc/289244
ER -

References

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  1. BRESSAN, ALDO (1962) - Metodo di assiomatizzazione in senso stretto della Meccanica classica, «Rend. Sem. Mat. Univ. Padova», 32, 55-212. Zbl0114.14902
  2. BRESSAN, ALDO e MONTANARO, ADRIANO (1982) - Axiomatic foundations of the kinematics common to classical physics and special relativity, «Rend. Sem. Mat. Univ. Padova», 68, 7-26. Zbl0538.70001MR702154
  3. BRESSAN, ALDO - Towards axiomatic foundations of the Mach Painlevé type for classical or relativistic theories of continuous media. Printed in the present review. Zbl0774.73003
  4. KELLOGG, OLIVER DIMON (1929) - Foundations of potential theory. Berlin, Verlag Von Julius Springer. MR222317
  5. MONTANARO, ADRIANO - A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 2: Alternative completion of Bressan's work, fit for extension to special relativity. Being printed. Zbl0774.73005

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