Geodesic
Infinite motion in the classical functional mechanics
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, pp. 222-232 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper the description of infinite movement in the functional formulation of classical mechanics is investigated. On the example of simple exactly solvable problems (passing through the barrier and falling in the center) the two classes of problems of scattering and singularity are considered. The functional mechanics corrections, arising from scattering, to the mean values and variance of canonical variables are calculated. In particular in the simplest case of transmission through the barrier the shift of the mean value coordinate by a constant arises , this constant depends on the parameters of the barrier, and logarithmic correction to the variance of the free motion coordinate. Also it is shown, that functional mechanics approach leads to the elimination of singularities in the kinetic energy of the falling in the center, which is equivalent to the solution of the Friedman equation in cosmology.
Keywords: classical mechanics,irreversibility problem, problem of scattering, problem of singularity, Friedman universe.
Mots-clés : Liouville equation 
@article{VSGTU_2013_130_1_a21,
     author = {A. I. Mikhailov},
     title = {Infinite motion in the classical functional mechanics},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {222--232},
     year = {2013},
     volume = {130},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a21/}
}
TY  - JOUR
AU  - A. I. Mikhailov
TI  - Infinite motion in the classical functional mechanics
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2013
SP  - 222
EP  - 232
VL  - 130
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a21/
LA  - ru
ID  - VSGTU_2013_130_1_a21
ER  - 
%0 Journal Article
%A A. I. Mikhailov
%T Infinite motion in the classical functional mechanics
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2013
%P 222-232
%V 130
%N 1
%U http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a21/
%G ru
%F VSGTU_2013_130_1_a21
A. I. Mikhailov. Infinite motion in the classical functional mechanics. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, pp. 222-232. http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a21/

[1] I. V. Volovich, “Time Irreversibility Problem and Functional Formulation of Classical Mechanics”, Vestnik SamGU. Estestvennonauchn. Ser., 2008, no. 8/1(67), 35–55

[2] I. V. Volovich, “Bogoliubov equations and functional mechanics”, Theoret. and Math. Phys., 164:3 (2010), 1128–1135 | DOI | DOI | Zbl

[3] N. N. Bogolyubov, Problems of Dynamical Theory in Statistical Physics, Gostekhizdat, Moscow, Leningrad, 1946, 119 pp. | MR

[4] A. S. Trushechkin, “Irreversibility and the role of an instrument in the functional formulation of classical mechanics”, Theoret. and Math. Phys., 164:3 (2010), 1198–1201 | DOI | DOI | Zbl

[5] I. V. Volovich, A. S. Trushechkin, “Functional Classical Mechanics and Rational Numbers”, p-Adic Numb. Ultr. Anal. Appl, 1:4 (2009), 361–367, arXiv: [math-ph] 0910.1502 | DOI | MR | Zbl

[6] E. V. Piscovskiy, I. V. Volovich,, “On the Correspondence Between Newtonian and Functional Mechanics”, Quantum Bio-Informatic IV, Quantum Probability and White Noise Analisis, 28, eds. L. Accardy, W. Freudenberg, M. Ohya, World Sci, Singapure, 2011, 363–372 | DOI | MR

[7] A. I. Mikhaylov, “Functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem”, p-Adic Numb. Ultr. Anal. Appl, 3:3 (2011), 205–211 | DOI | DOI | MR | Zbl

[8] O. V. Groshev, “Liouville operator and functional mechanics”, The Third International Conference “Mathematical Physics and Its Applications”, Book of Abstracts (August 27 – September 01, 2012 Samara, Russia), eds. I. V. Volovich, V. P. Radchenko, Samara State Technical Univ., Samara, 2012, 105

[9] I. V. Volovich, “Functional mechanics and black holes”, The Third International Conference “Mathematical Physics and Its Applications”, Book of Abstracts (August 27 – September 01, 2012 Samara, Russia), eds. I. V. Volovich, V. P. Radchenko, Samara State Technical Univ., Samara, 2012, 92

[10] C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W. H. Freeman, San Francisco, 1973, 1215 pp. ; Ch. Mizner, K. Torn, Dzh. Uiler, Gravitatsiya, v 3-kh t, Mir, M., 1977 (T. 1, 480 c.; T. 2, 527 c.; T. 3, 512 c.) | MR

[11] V. V. Kozlov, Thermal equilibrium in the sense of Gibbs and Poincaré, Institut Komp'yuternykh Issledovanij, Moscow, Izhevsk, 2002, 320 pp. | MR | Zbl