ISSN:
1420-9039
Keywords:
34D20
;
34D35
;
35Q72
;
73H10
;
73K03
;
Elastic string
;
stability
;
energy-momentum
;
axial motion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00915277
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