# 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

- Volume: 81, Issue: 1, page 47-54
- 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 2. Alternative completion of Bressan's work, fit for extension to special relativity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 81.1 (1987): 47-54. <http://eudml.org/doc/287286>.

@article{Montanaro1987,

abstract = {The work [3] of axiomatization of various classical theories on continuous bodies from the Mach-Painlevè point of view, is completed here in a way which -unlike [4]- 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 [1], 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 1, the Euclidean physical metric on inertial spaces is consequently determined, without introducing it as a primitive notion. The treatment of Part 2 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 [3].},

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; equivalence; affine inertial frames; isotropic inertial frames; Galilean transformation; Euclidean physical metric},

language = {eng},

month = {3},

number = {1},

pages = {47-54},

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 2. Alternative completion of Bressan's work, fit for extension to special relativity},

url = {http://eudml.org/doc/287286},

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 2. Alternative completion of Bressan's work, fit for extension to special relativity

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 - 47

EP - 54

AB - The work [3] of axiomatization of various classical theories on continuous bodies from the Mach-Painlevè point of view, is completed here in a way which -unlike [4]- 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 [1], 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 1, the Euclidean physical metric on inertial spaces is consequently determined, without introducing it as a primitive notion. The treatment of Part 2 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 [3].

LA - eng

KW - Axiomatization; Continuum; Thermodynamics; equivalence; affine inertial frames; isotropic inertial frames; Galilean transformation; Euclidean physical metric

UR - http://eudml.org/doc/287286

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 and 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 relativiste theories of continuous media. Printed in the present review. Zbl0774.73003
- 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. Printed in the present review. Zbl0774.73004

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