An experimental study of Goldstein-Petrich curves
Emilio Musso · 2009
Abstract. Numerical methods are used to prove the existence of closed embedded curves in R 2 and H 2 whose shapes are invariant under the Goldstein–Petrich flow. Numerical routines are used to compute all closed spherical free elasticæ. The evidence of the experiments shows the existence of a unique, up to rotations, embedded closed free elastica of S 2 with symmetry group of order h, for every positive integer h ≥ 2. The order of the symmetry groups and the number of self-intersection points of any closed free elastica in S 2 are determined. 1.