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Elastic curves on the sphere

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Abstract

This paper deals with the derivation of equations suitable for the computation of elastic curves on the sphere. To this end, equations for the main invariants of spherical elastic curves are given. A new method for solving geometrically constraint differential equations is used to compute the curves for given initial values. A classification of the fundamental forms of the curves is presented.

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Authors and Affiliations

  1. FB Informatik, Universität Kaiserslautern, Postfach 3049, 6750, Kaiserslautern, Germany

    Guido Brunnett

  2. Center for Systems Science and Engineering, Arizona State University, 85287, Tempe, AZ, USA

    Peter E. Crouch

Authors
  1. Guido Brunnett
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  2. Peter E. Crouch
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Brunnett, G., Crouch, P.E. Elastic curves on the sphere. Adv Comput Math 2, 23–40 (1994). https://doi.org/10.1007/BF02519034

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  • DOI: https://doi.org/10.1007/BF02519034

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