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

Abstract

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