Variationality of geodesic circles in two dimensions
  This note treats the notion of Lagrange derivative for the third order mechanics in the context of covariant Riemannian geometry. The variational differential equation for geodesic circles in two dimensions is obtained. The influence of the curvature tensor on the Lagrange derivative leads to the emergence of the notion of quasiclassical spin in the pseudo-Riemannian case. 
R. Ya. Matsyuk
math.DG gr-qc math-ph math.MP