Infinite motion in the classical functional mechanics
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....
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2013-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/34709/23060 |
| _version_ | 1811330255047098368 |
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| author | Andrey Igorevich Mikhailov |
| author_facet | Andrey Igorevich Mikhailov |
| author_sort | Andrey Igorevich Mikhailov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T15:58:37Z |
| format | Article |
| id | doaj.art-3b1091d531f34a658e8bf5ecf3316e91 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:58:37Z |
| publishDate | 2013-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-3b1091d531f34a658e8bf5ecf3316e912022-12-22T02:40:36ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812013-12-0117122223210.14498/vsgtu121531222Infinite motion in the classical functional mechanicsAndrey Igorevich Mikhailov0Steklov Mathematical Institute of Russian Academy of SciencesIn 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.https://journals.eco-vector.com/1991-8615/article/viewFile/34709/23060classical mechanicsirreversibility problemliouville equationproblem of scatteringproblem ofsingularityfriedman universe |
| spellingShingle | Andrey Igorevich Mikhailov Infinite motion in the classical functional mechanics Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki classical mechanics irreversibility problem liouville equation problem of scattering problem ofsingularity friedman universe |
| title | Infinite motion in the classical functional mechanics |
| title_full | Infinite motion in the classical functional mechanics |
| title_fullStr | Infinite motion in the classical functional mechanics |
| title_full_unstemmed | Infinite motion in the classical functional mechanics |
| title_short | Infinite motion in the classical functional mechanics |
| title_sort | infinite motion in the classical functional mechanics |
| topic | classical mechanics irreversibility problem liouville equation problem of scattering problem ofsingularity friedman universe |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/34709/23060 |
| work_keys_str_mv | AT andreyigorevichmikhailov infinitemotionintheclassicalfunctionalmechanics |