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

© 2016 Universitá del Salento. 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).