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An impetus-striction simulation of the dynamics of an elastica

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Summary

This article concerns the three-dimensional, large deformation dynamics of an inextensible, unshearable rod. To enforce the conditions of inextensibility and unshearability, a technique we call the impetus-striction method is exploited to reformulate the constrained Lagrangian dynamics as an unconstrained Hamiltonian system in which the constraints appear as integrals of the evolution. We show here that this impetus-striction formulation naturally leads to a numerical scheme which respects the constraints and conservation laws of the continuous system. We present simulations of the dynamics of a rod that is fixed at one end and free at the other.

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Authors and Affiliations

  1. Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA

    D. J. Dichmann & J. H. Maddocks

  2. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    D. J. Dichmann & J. H. Maddocks

Authors
  1. D. J. Dichmann
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  2. J. H. Maddocks
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Additional information

Communicated by Jerrold Marsden and Stephen Wiggins

Dedication: Juan Simo and I shared many common interests in Hamiltonian systems, stability analyses, and the theory of rods. We rarely agreed on the best way of viewing problems, but we both always enjoyed debating the issues. He would undoubtedly have held strong opinions about this article, which is dedicated to him. He is sorely missed.

This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.

Research supported by the NSF, NASA GSFC and Computer Sciences Corporation.

Research supported by AFOSR and ONR.

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Dichmann, D.J., Maddocks, J.H. An impetus-striction simulation of the dynamics of an elastica. J Nonlinear Sci 6, 271–292 (1996). https://doi.org/10.1007/BF02439312

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  • DOI: https://doi.org/10.1007/BF02439312

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