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Locking constraints for elastic rods and a curvature bound for spatial curves

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Abstract

The paper presents necessary conditions for curves in R3 subject to the nonholonomic constraint of an upper bound for curvature and suitable boundary conditions. The proof essentially uses a reformulation of the problem by means of framed curves. The Euler–Lagrange equations for nonlinearly elastic Cosserat rods subject to a general class of locking constraints is derived by similar methods.

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany

    Friedemann Schuricht

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  1. Friedemann Schuricht
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Mathematics Subject Classification (2000) 49K15, 51M16, 74B20, 74K10

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Schuricht, F. Locking constraints for elastic rods and a curvature bound for spatial curves. Calc. Var. 24, 377–402 (2005). https://doi.org/10.1007/s00526-005-0322-0

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  • DOI: https://doi.org/10.1007/s00526-005-0322-0

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