# 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

- Volume: 81, Issue: 1, page 35-46
- ISSN: 1120-6330

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topMontanaro, 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 Lincei. Matematica e Applicazioni 81.1 (1987): 35-46. <http://eudml.org/doc/287423>.

@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 Lincei. Matematica e Applicazioni},

keywords = {Axiomatization; Continuum; Thermodynamics; classical kinematics; gravitational isotropy; isotropic inertial frames; Galilean transformation; Euclidean physical metric},

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/287423},

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 Lincei. Matematica e Applicazioni

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; classical kinematics; gravitational isotropy; isotropic inertial frames; Galilean transformation; Euclidean physical metric

UR - http://eudml.org/doc/287423

ER -

## References

top- BRESSAN, ALDO (1962) - Metodo di assiomatizzazione in senso stretto della Meccanica classica, «Rend. Sem. Mat. Univ. Padova», 32, 55-212. Zbl0114.14902
- 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
- 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
- KELLOGG, OLIVER DIMON (1929) - Foundations of potential theory. Berlin, Verlag Von Julius Springer. MR222317
- 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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