Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2020, Number 5, Pages 50–56 (Mi vmumm4353)  
This article is cited in 2 scientific papers (total in 2 papers)

Mechanics

On the motion of a system with a moving internal element in the presence of external viscous friction

E. I. Kugushev, T. V. Popova, S. V. Sazonov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (314 kB) Citations (2)
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Abstract: We consider a system consisting of a translationally moving platform along a fixed line with viscous friction and a body committing a given translational motion relatively to the platform due to internal forces along the same line. In relative motion the value of the body velocity is limited. It is proved that, in the case of linear viscous friction, the unlimited displacement of the platform in any direction is impossible. In the general case under certain conditions imposed on the force of viscous friction, the velocity of the platform is limited. At the same time, if the displacement of the platform in any direction, for example to the right, is unlimited, then with the growth of time the value of the platform velocity changes its sign infinite number of times, and the total time of platform motion to the left and the path passed at the same time tend to infinity.
Key words: viscous friction, moving internal mass, unlimited movement.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00887
Received: 18.09.2019
English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2020, Volume 75, Issue 5, Pages 140–146
DOI: https://doi.org/10.3103/S0027133020050027
Bibliographic databases:
Document Type: Article
UDC: 531.01
Language: Russian
Citation: E. I. Kugushev, T. V. Popova, S. V. Sazonov, “On the motion of a system with a moving internal element in the presence of external viscous friction”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2020, no. 5, 50–56; Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 75:5 (2020), 140–146
Citation in format AMSBIB
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