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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, Issue 1(30), Pages 222–232 (Mi vsgtu1215)  

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Mechanics and Classical Field Theory

Infinite motion in the classical functional mechanics

A. I. Mikhailovab

a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, 119991, Russia
b Russian Federal Research Institute of Fisheries and Oceanography, Moscow, 107140, Russia

Abstract: 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, Liouville equation, problem of scattering, problem of singularity, Friedman universe

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 2928.2012.1


DOI: https://doi.org/10.14498/vsgtu1215

Full text: PDF file (193 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.958
MSC: 82C05
Original article submitted 17/I/2013
revision submitted – 26/II/2013

Citation: A. I. Mikhailov, “Infinite motion in the classical functional mechanics”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 222–232

Citation in format AMSBIB
\Bibitem{Mik13}
\by A.~I.~Mikhailov
\paper Infinite motion in the classical functional mechanics
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 222--232
\mathnet{http://mi.mathnet.ru/vsgtu1215}
\crossref{https://doi.org/10.14498/vsgtu1215}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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