### Abstract

The stability of twisted straight rods is described within the framework of the time dependent Kirchhoff equations for thin elastic filaments. A perturbation method is developed to study the linear stability of this problem and find the dispersion relations. A nonlinear analysis results in a new amplitude equation, describing the deformation of the rod beyond the instability, which takes the form of a pair of nonlinear, second-order evolution equations coupling the local deformation amplitude to the twist density. Various solutions, such as solitary waves, are presented.

Original language | English (US) |
---|---|

Pages (from-to) | 3537-3540 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 77 |

Issue number | 17 |

State | Published - 1996 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*77*(17), 3537-3540.

**New amplitude equations for thin elastic rods.** / Goriely, Alain; Tabor, Michael.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 77, no. 17, pp. 3537-3540.

}

TY - JOUR

T1 - New amplitude equations for thin elastic rods

AU - Goriely, Alain

AU - Tabor, Michael

PY - 1996

Y1 - 1996

N2 - The stability of twisted straight rods is described within the framework of the time dependent Kirchhoff equations for thin elastic filaments. A perturbation method is developed to study the linear stability of this problem and find the dispersion relations. A nonlinear analysis results in a new amplitude equation, describing the deformation of the rod beyond the instability, which takes the form of a pair of nonlinear, second-order evolution equations coupling the local deformation amplitude to the twist density. Various solutions, such as solitary waves, are presented.

AB - The stability of twisted straight rods is described within the framework of the time dependent Kirchhoff equations for thin elastic filaments. A perturbation method is developed to study the linear stability of this problem and find the dispersion relations. A nonlinear analysis results in a new amplitude equation, describing the deformation of the rod beyond the instability, which takes the form of a pair of nonlinear, second-order evolution equations coupling the local deformation amplitude to the twist density. Various solutions, such as solitary waves, are presented.

UR - http://www.scopus.com/inward/record.url?scp=0012920014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012920014&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0012920014

VL - 77

SP - 3537

EP - 3540

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 17

ER -