Geodesic
On dynamics of relational systems: non-relativistic case
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 1, pp. 99-112.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper presents a general method to obtain the dynamic equation for the theory constructed on the basis of a dualistic paradigm. For example, the applications of this technique to the cases of the general theory of relativity and the quantum theory are considered. The initial (the first and partially the second) stages of this method as applied to the relational physics are discussed. Assumptions regarding the limit for a relational theory dynamic equation are suggested. It is shown that in the non-relativistic case it describes the dynamics of the metrics of the three-dimensional space in the reference frame, based on a continuum of arbitrarily moving material points.
Keywords: space-time, reference system, relational physics. 
@article{CHFMJ_2017_2_1_a9,
     author = {A. G. Zhilkin},
     title = {On dynamics of relational systems: non-relativistic case},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {99--112},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a9/}
}
TY  - JOUR
AU  - A. G. Zhilkin
TI  - On dynamics of relational systems: non-relativistic case
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2017
SP  - 99
EP  - 112
VL  - 2
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a9/
LA  - ru
ID  - CHFMJ_2017_2_1_a9
ER  - 
%0 Journal Article
%A A. G. Zhilkin
%T On dynamics of relational systems: non-relativistic case
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2017
%P 99-112
%V 2
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a9/
%G ru
%F CHFMJ_2017_2_1_a9
A. G. Zhilkin. On dynamics of relational systems: non-relativistic case. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 1, pp. 99-112. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a9/

[1] Yu.S. Vladimirov, Metaphysics, Binom. Laboratoriya znaniy Publ., Moscow, 2009, 568 pp. (In Russ.)

[2] A.G. Zhilkin, “Basic categories and principles of relational physics”, Bulletin of Chelyabinsk State University, 25 (316) (2013), 80–92 (In Russ.)

[3] A.G. Zhilkin, “Relational physics from the view-point of metaphysics”, Metaphysics, 2 (12) (2014), 49–67 (In Russ.)

[4] C.W. Misner , K.S. Thorne, J.A. Wheeler, Gravitation, Freeman, San Francisco, 1973, 1304 pp. | MR | MR

[5] L.D. Landau, E.M. Lifshitz, The Classical Theory of Field, Heinemann, Oxford–Butterworth, 1975 | MR | MR

[6] L.D. Landau, E.M. Lifshitz, Mechanics, Heinemann, Oxford–Butterworth, 1976 | MR | MR

[7] P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, New York, 1958, 312 pp. | MR | MR | Zbl

[8] L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Pergamon Press, Oxford, 1977 | MR

[9] Yu.S. Vladimirov, Reference frames in theory of gravity, Energoizdat Publ., Moscow, 1982, 256 pp. (In Russ.) | MR

[10] L.I. Sedov, Mechanics of continuous media, World Scientific Publ., 1997, 1310 pp. | MR | MR | Zbl