The Evolution of the Local Induction Approximation for a Regular Polygon

  1. de la Hoz, Francisco 1
  2. Vega, Luis 1
  1. 1 Universidad del País Vasco/Euskal Herriko Unibertsitatea
    info

    Universidad del País Vasco/Euskal Herriko Unibertsitatea

    Lejona, España

    ROR https://ror.org/000xsnr85

Actes de conférence:
ESAIM: Proceedings and Surveys

ISSN: 2267-3059

Année de publication: 2014

Volumen: 45

Pages: 447-455

Type: Communication dans un congrès

DOI: 10.1051/PROC/201445046 GOOGLE SCHOLAR lock_openAccès ouvert editor

Résumé

In this paper, we consider the so-called local induction approximation (LIA): Xt = Xs ^ Xss, where ^ is the usual cross product, and s denotes the arc-length parametrization. We study its evolution, taking planar regular polygons of M sides as initial data. Assuming uniqueness and bearingin mind the invariances and symmetries of the problem, we are able to fully characterize, by algebraic means, X(s, t) and its derivative, the tangent vector T(s, t), at times t which are rational multiples of 2/M2. We show that the values at those instants are intimately related to the generalized quadratic Gauß sums.