The Kirchhoff Rod as a XY Spin Chain Model
  A XY Heisenberg spin chain model with two perpendicular spins par site is mapped onto a Kirchhoff thin elastic rod. It is shown that in the case of constant curvature the Euler--Lagrange equation leads to the static sine-Gordon equation. The kink-antikink type and periodical static solutions for these models are derived. 
Rossen Dandoloff, Georgi Grahovski