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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2003, Volume 10, Number 3, Pages 301–306
(Mi jmag252)
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About the string with beads
A. D. Myshkis, A. M. Filimonov Moscow State University of Communications, 15 Obraztsova Str., Moscow, 127994, Russia
Abstract:
We consider a classical problem of free oscillations of the elastic weightless string with $N$ beads which has been originally studied by Lagrange. We prove that for $N$ being prime or a power of $2$ the maximal displacement of the bead from its equilibrium position increases to infinity as $N\to\infty$ while the total energy of system remains bounded by independent on $N$ constant.
Received: 08.04.2003
Citation:
A. D. Myshkis, A. M. Filimonov, “About the string with beads”, Mat. Fiz. Anal. Geom., 10:3 (2003), 301–306
Linking options:
https://www.mathnet.ru/eng/jmag252 https://www.mathnet.ru/eng/jmag/v10/i3/p301
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