Filimonov, A. M.; Myshkis, A. D. On properties of large wave effect in classical problem of bead string vibration. (English) Zbl 1329.74069 J. Difference Equ. Appl. 10, No. 13-15, 1171-1175 (2004). Summary: We consider a classical problem of free oscillations of the elastic weightless string with \(N+1\) beads which has been originally studied by Lagrange. It is proved that for \(N\) being prime or a power of \(2\), the maximal displacement of the bead from its equilibrium position increases logarithmically to infinity. Cited in 6 Documents MSC: 74F05 Thermal effects in solid mechanics 34D05 Asymptotic properties of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations 39A12 Discrete version of topics in analysis 74H45 Vibrations in dynamical problems in solid mechanics PDFBibTeX XMLCite \textit{A. M. Filimonov} and \textit{A. D. Myshkis}, J. Difference Equ. Appl. 10, No. 13--15, 1171--1175 (2004; Zbl 1329.74069) Full Text: DOI References: [1] Myshkis AD, Journal Matematicheskaya Fizika, Analiz i Geometriya [2] Lagrange GL, Mechanique Analitique (1788) [3] Kurchanov PF, Prikladnaya Matematika i Mekhanika 55 pp 989– (1991) [4] Filimonov AM, Computes Rendus Acad. Sci. Parisv. 313 pp 961– (1991) [5] DOI: 10.1080/10236199808808125 · Zbl 0907.34050 · doi:10.1080/10236199808808125 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.