Stability of axial motions of nonlinearly elastic loops |
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Authors: | Timothy J Healey |
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Institution: | (1) Dept. of Theoretical & Applied Mechanics, Center for Applied Mathematics, Kimball Hall, 14853 Ithaca, NY, USA |
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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. |
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Keywords: | 34D20 34D35 35Q72 73H10 73K03 |
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