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Heavy rotating string—a nonlinear eigenvalue problem

✍ Scribed by Ignace I. Kolodner

Publisher
John Wiley and Sons
Year
1955
Tongue
English
Weight
500 KB
Volume
8
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

Rotations of a heavy string with one endpoint free are considered. According to the linear theory, a string of a given length can rotate only at certain eigenvelocities of rotation w~1~ which form a discrete spectrum. It is shown that according to the more accurate non‐linear theory, a string can rotate at any velocity ω > ω~1~, and that for each w in the range ω~n~ < ω < ω~n+1~ there are exactly n distinct modes of rotation.

📜 SIMILAR VOLUMES

A NON-LINEAR EIGENVALUE PROBLEM ASSOCIAT
A NON-LINEAR EIGENVALUE PROBLEM ASSOCIATED WITH INEXTENSIBLE WHIRLING STRINGS
✍ J. COOMER; M. LAZARUS; R.W. TUCKER; D. KERSHAW; A. TEGMAN 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 288 KB

The motion of idealized inextensible strings is discussed. The equations of motion are analyzed for closed-loop con"gurations, free of body forces and open hanging strings whirling under gravity. The latter give rise to an interesting non-linear eigenvalue problem describing a spectrum of whirling m