Geometric characterization of the rotation centers of a particle in a flow

We provide a geometrical characterization of the instantaneous rotation centers→O(p, t) of a particle in a flow F over time t. Specifically, we will prove that: a) at a specific instant t, the point→O(p, t) is the center of curvature at the vertex of the parabola which best fits the path-particle line γ(t) on its Darboux plane at p, and b) over time t, the geometrical locus of→O(p, t) is the line of striction of the principal normal surface generated by γ(t).